Question
Use polynomial identities to multiply the expressions ?
![open parentheses 25 straight x squared minus 15 straight y squared close parentheses open parentheses 25 straight x squared plus 15 straight y squared close parentheses](data:image/png;base64,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)
The correct answer is: Thus, the product is (25x^2-15y^2)(25x^2+15y^2)=625x^4-225y^4.
ANSWER:
Hint:
, where a and b can be real values, variables or multiples of both.
We are asked to use polynomial identities to find the product of the expression.
Step 1 of 2:
The given expression is
.![text It is of the form end text left parenthesis a minus b right parenthesis left parenthesis a plus b right parenthesis text where end text a equals 25 x squared straight & b equals 15 y squared text . end text](data:image/png;base64,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)
Step 2 of 2:
Use the polynomial identity
to find the product of the expression;
![table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell open parentheses 25 x squared minus 15 y squared close parentheses open parentheses 25 x squared plus 15 y squared close parentheses equals open parentheses 25 x squared close parentheses squared minus open parentheses 15 y squared close parentheses squared end cell row cell equals 625 x to the power of 4 minus 225 y to the power of 4 space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space end cell end table](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAWgAAAAxCAYAAAD3EzNeAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAdoyL+RwAABtpJREFUeNrtnV9kH1kUx6+IiLXKqqjqQ4mqqopQtaKqL1FRFVUqIlZViFW1oi/7VH2oUvuQp76s6kNVlVqrKqJEHyqiQlRUH2rZx33tw1oRP2H2nM756WRyZ3Ln3507934/HH7z+83vz/meO2fuPXN/c5UCAIB6icR6ZOtkJyAJ9AEAuMUA2S2yD5AC+gAA3GQHEvitj69DAh/8QmwwHM/jItk76BOGPr4OCXzwC7HBcDzNUUlao9CnGX34Cx9iSNCKXw9Ff8Sme7Gpgy7EN0+Hk2TLkoRC0smaPmNk7x1sIL4OmXR+rUscEJvuxKYOuhRfnQ6cdFbIDjX8e1zTyao+/MHjie3zZH+Q/aviessW2ZzmfVGOVcXGkInPbHfFP2XJvyy/zpKtITadik0ddCm+Oh04+ZyykBDTOnWlnVTWZ1y+LAmfGWbJvpft07LPrMb5pg5OG0OmZ2QLOX5Elv1akyAjNu7Hpg66GN+0Dk2cIEx06ko7qazPb2S3DfY7TvbRQiOxNWQy8SOy7Ncvam+NzafYRJ7Fpg66GN8mdKhDJ2/byRuyC4b77lRwfj7jh9+X12wPmeoM7hOyGc3zi2QPCvg1QfbW09hEnsUm1GOvCR3q0MnbdsK1riGD/SY0w4yiBx1PSzmS2L5J9sigZuR6gr4hZ/kk35H9RXa4gF9DEg8fYxN5FpuDdDHRqYvxzdOhKUx06kI7KcWuwT7DZBsqvoCRdr4nP4jPLnfUt9qZjimyJXk82cKZuExwTfy7TPYy9dw9FV+8KErP09hEnsUm5GOvZ/n43A25nRzk/A9kr8gu5ewzqOLCODvz+YBhwKqKp6hsJc5MVQ76Mj2XosnjIP/Yj0+J7RGyv+XgajJBIzbtxSbkY69nuU3shtxO8oYPo9JAivylkRtT3vzYRXGgqXmlTffusvzbTjxeEj+LUqTE0bXYRJ7FpukSh6vx7VqJw6V2UopVzfBJyRnmsdRhipL1D7P+HE92frajCTrLvzU5qEblzDtQ4nekLzD4FJvIs9iEeuy1cZEwS6cg2oluCssRqccMlvi8M+KcrkfwWhod14A2axhGt5E8svx7SjZN9pzsp5K/47bae6HCp9hEnsUm1GOvCR3K6BRMO9FNAl9WZtOp/pQzxoDYlDh+LbUf13NWUo3iioonmbucoE396w8fearOxwq/w+SPKl2NTeRZbEI99prQoYxOIbWTr/9xH0s5a1JLu67iaShcxP8iZ/5zmpoMi3RM870vRLA2E3NV//pclfdPl/wtWX8nRmzcjU1ox16TOhTVKah24uoNW7rEdEUNu3azJMQmvGOvSR1c0MnldqJ+Vm7e8rArrMhQqgxcs1pAbDoZm1COPRs6tK2T6+0ElIQvOixDBsQGoJ0AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAGWZU3aW5IL/AABQAP7n0XrACSp0/wEAjsJLEfFNVY4FmqBC9x8A4DC8MkX/pioR/AcAhATfr5Xv28pre/HSNLwaxMXE6/3le/h1XmONF8Gc03xO1QVLdfyq9q620ESCMvWvDR1s+A8AcJQFScgnZfuQJJ3kjbB5wUdeV62/fPppFddDZzWJqW7qTvg6TP1rQwcb/gMAHIQTzGbJ9x5X+5eqsZE4bCUnnX8u6IDkDEAg/K6qrTi8UyF5zCv9zcDvy2suJKidhnXg9dhmNM/zWm0PkKAB8IPIwHR8Jjta8jsn1P6FJYsmjw8qXlW5z02yR470IHX+1a3DDbV/RWJeCZrXdDuMBA1A2HDPj2vPvNDltoovfHHJY+6A9w2Tbaj4olk6efBn8EU0Xs7mjvpWr9XBi2guyeNJsreO6JLlX906XFbxxdkk98juomkCACLpxXKiGFTxMunnpQd3K+M9PCf3FdmlnM/lzzoriYZ76XnL2q+qeMbIVk6vsemRRFH/6tKB/f2U2B5R8RL1w2iaAKDEwT083RLx42T/aJ4flaR0osBv4wT2Luf1Reltjjmgo6l/deqwnXi8JHoAAMDX4fdAxmu91Db3/h6ruEZappSioz+vmBPTbMtamPpXtw5rkvBHpfc8gGYJAFBSxpjJSEIbiW2+kPdShuxFOSOJR9cLfS2JjuuzmzWUOMpi6l8TOjwlmyZ7rvb+IQUAEDhDMuyeTySdH1U8r3cysd+yyq8j9+GLjRPSC2SbkqR0LbXfiPTekwn5CtmzlnQw9a9uHZSUNJ4osznXAIDAGJEh+39ku5KwL6T2Ma1tX1fxBUb+nC/S2zynOSlwAtPVvl9IMrONqX916tDnqrx/Gk0RAADcghPze8gAAADuwaWeCcgAAABuwRcOlyEDAPb5HyvkoTo6nsFcAAAGonRFWHRNYXRoTUwAPG1hdGggeG1sbnM9Imh0dHA6Ly93d3cudzMub3JnLzE5OTgvTWF0aC9NYXRoTUwiPjxtdGFibGUgY29sdW1uYWxpZ249InJpZ2h0IGxlZnQgcmlnaHQgbGVmdCByaWdodCBsZWZ0IHJpZ2h0IGxlZnQgcmlnaHQgbGVmdCByaWdodCBsZWZ0IiBjb2x1bW5zcGFjaW5nPSIwZW0gMmVtIDBlbSAyZW0gMGVtIDJlbSAwZW0gMmVtIDBlbSAyZW0gMGVtIj48bXRyPjxtdGQ+PG1mZW5jZWQgc2VwYXJhdG9ycz0ifCI+PG1yb3c+PG1uPjI1PC9tbj48bXN1cD48bWk+eDwvbWk+PG1uPjI8L21uPjwvbXN1cD48bW8+JiN4MjIxMjs8L21vPjxtbj4xNTwvbW4+PG1zdXA+PG1pPnk8L21pPjxtbj4yPC9tbj48L21zdXA+PC9tcm93PjwvbWZlbmNlZD48bWZlbmNlZCBzZXBhcmF0b3JzPSJ8Ij48bXJvdz48bW4+MjU8L21uPjxtc3VwPjxtaT54PC9taT48bW4+MjwvbW4+PC9tc3VwPjxtbz4rPC9tbz48bW4+MTU8L21uPjxtc3VwPjxtaT55PC9taT48bW4+MjwvbW4+PC9tc3VwPjwvbXJvdz48L21mZW5jZWQ+PG1vPj08L21vPjxtc3VwPjxtZmVuY2VkIHNlcGFyYXRvcnM9InwiPjxtcm93Pjxtbj4yNTwvbW4+PG1zdXA+PG1pPng8L21pPjxtbj4yPC9tbj48L21zdXA+PC9tcm93PjwvbWZlbmNlZD48bW4+MjwvbW4+PC9tc3VwPjxtbz4mI3gyMjEyOzwvbW8+PG1zdXA+PG1mZW5jZWQgc2VwYXJhdG9ycz0ifCI+PG1yb3c+PG1uPjE1PC9tbj48bXN1cD48bWk+eTwvbWk+PG1uPjI8L21uPjwvbXN1cD48L21yb3c+PC9tZmVuY2VkPjxtbj4yPC9tbj48L21zdXA+PC9tdGQ+PC9tdHI+PG10cj48bXRkPjxtbz49PC9tbz48bW4+NjI1PC9tbj48bXN1cD48bWk+eDwvbWk+PG1uPjQ8L21uPjwvbXN1cD48bW8+JiN4MjIxMjs8L21vPjxtbj4yMjU8L21uPjxtc3VwPjxtaT55PC9taT48bW4+NDwvbW4+PC9tc3VwPjxtbz4mI3hBMDs8L21vPjxtbz4mI3hBMDs8L21vPjxtbz4mI3hBMDs8L21vPjxtbz4mI3hBMDs8L21vPjxtbz4mI3hBMDs8L21vPjxtbz4mI3hBMDs8L21vPjxtbz4mI3hBMDs8L21vPjxtbz4mI3hBMDs8L21vPjxtbz4mI3hBMDs8L21vPjxtbz4mI3hBMDs8L21vPjxtbz4mI3hBMDs8L21vPjxtbz4mI3hBMDs8L21vPjxtbz4mI3hBMDs8L21vPjxtbz4mI3hBMDs8L21vPjxtbz4mI3hBMDs8L21vPjxtbz4mI3hBMDs8L21vPjxtbz4mI3hBMDs8L21vPjxtbz4mI3hBMDs8L21vPjxtbz4mI3hBMDs8L21vPjxtbz4mI3hBMDs8L21vPjxtbz4mI3hBMDs8L21vPjxtbz4mI3hBMDs8L21vPjxtbz4mI3hBMDs8L21vPjxtbz4mI3hBMDs8L21vPjxtbz4mI3hBMDs8L21vPjxtbz4mI3hBMDs8L21vPjxtbz4mI3hBMDs8L21vPjxtbz4mI3hBMDs8L21vPjxtbz4mI3hBMDs8L21vPjxtbz4mI3hBMDs8L21vPjxtbz4mI3hBMDs8L21vPjxtbz4mI3hBMDs8L21vPjxtbz4mI3hBMDs8L21vPjxtbz4mI3hBMDs8L21vPjxtbz4mI3hBMDs8L21vPjxtbz4mI3hBMDs8L21vPjxtbz4mI3hBMDs8L21vPjxtbz4mI3hBMDs8L21vPjxtbz4mI3hBMDs8L21vPjxtbz4mI3hBMDs8L21vPjxtbz4mI3hBMDs8L21vPjxtbz4mI3hBMDs8L21vPjxtbz4mI3hBMDs8L21vPjxtbz4mI3hBMDs8L21vPjxtbz4mI3hBMDs8L21vPjxtbz4mI3hBMDs8L21vPjxtbz4mI3hBMDs8L21vPjxtbz4mI3hBMDs8L21vPjxtbz4mI3hBMDs8L21vPjxtbz4mI3hBMDs8L21vPjxtbz4mI3hBMDs8L21vPjwvbXRkPjwvbXRyPjwvbXRhYmxlPjwvbWF0aD6ALB1iAAAAAElFTkSuQmCC)
Note:
Polynomial identities are equations that are true for all possible values of the variable. We can perform polynomial multiplication by applying the distributive property to the multiplication of polynomials.
Related Questions to study
How can you use polynomial identities to factor polynomials and simplify numerical expressions ?
![12 cubed plus 2 cubed](data:image/png;base64,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)
How can you use polynomial identities to factor polynomials and simplify numerical expressions ?
![12 cubed plus 2 cubed](data:image/png;base64,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)
Use Pascal triangle to expand ![left parenthesis x plus y right parenthesis to the power of 5](data:image/png;base64,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)
The answer cam also be found by expanding the formula of 5Cr .
Use Pascal triangle to expand ![left parenthesis x plus y right parenthesis to the power of 5](data:image/png;base64,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)
The answer cam also be found by expanding the formula of 5Cr .
Use polynomial identities to multiply the expressions ?
![open parentheses 3 x squared minus 4 x y close parentheses open parentheses 3 x squared plus 4 x y close parentheses](data:image/png;base64,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)
Use polynomial identities to multiply the expressions ?
![open parentheses 3 x squared minus 4 x y close parentheses open parentheses 3 x squared plus 4 x y close parentheses](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAKoAAAATCAYAAAAAs5Y/AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAQ3ZOC+gAAAsRJREFUeNrtmt9HZkEYx0dWstaSZKWLJUkXeUVXyUp0sdZ6ZUm6SFastV7r/QfSRZbsRfaim73Yi7XWktVF8ookySuRJCuJtf9DF0mW2e8cz8sYM+fMeTtn3jPtPHx5z3vmzDzzmV/PzDmMuTVOuoXqUD8LFpgW2Nqgd9BJQBGYNmOioisOy7u5B8xWiFtg6ohpCTp06Mw4tH9PBnid+AWm+TONbgxL1xNQDbqmUXoJfYK6MnCih8rrc1DhlxTD5Wkj0EFgmj/TYaqkbHvQK6hdSbd9RwcGoC0Cm7c9gs4dQGUEdSQwzZUp+whVLB++uuOoFzPKY0fLx2dowRHU90os6gNT7hnTaEQ/s3hQLCsXmv8XDBuGZbrXMAF00FEnHYN2ExrExu8v0IwmTRX6IF2PSuX5wpR7xjQa0e0xDj6BXlNM9cKQ5oTSNUykX9OAUZWHibqcQU8tGiTJ73maHWV7SCy6lDKvPGPKPWPK/sZURFY1xrnn0Cr9nlRHQguONyqWDZLkt+hE68p/S9CiJq9bz5hyz5gaoTasE5qCjugIxGQ7dP80g50stxAzHAnVUzZInN/i+pd03Q39hjqa7KiBafNME5cpecd3FHO/ShmXWjibCv/6U0JN8vta+r1qmAXTLv1FYMo9Yxr1/jFLp29iAu2fVOhsCztq2hnDxu8D2vT00chv06RRA38fmHLPmFofpZQo4NXtXDcpIBYzxDHL5hA77wax9fsrVIa+Q3OGvCrKBsEHptwzptrDafEqbhp6QL1dvFX5Qzs2psQXNcUZ8ebiW8E7ahq/q3SkchZThs2Bf9GYcs+YRnaoxBPiDHCLliWhPSpUjSE2oF5NIT9o91fEjprW7ynKo2zI3/QKNTDNnqnzDyh8snICm6J8lPI/MI3sLXP7SZovVqPAXmcihnoT82xgmj3TYBobouU6WAuZ/gOiK0S6F0rrxwAAAUp0RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIj48bWZlbmNlZCBzZXBhcmF0b3JzPSJ8Ij48bXJvdz48bW4+MzwvbW4+PG1zdXA+PG1pPng8L21pPjxtbj4yPC9tbj48L21zdXA+PG1vPiYjeDIyMTI7PC9tbz48bW4+NDwvbW4+PG1pPng8L21pPjxtaT55PC9taT48L21yb3c+PC9tZmVuY2VkPjxtZmVuY2VkIHNlcGFyYXRvcnM9InwiPjxtcm93Pjxtbj4zPC9tbj48bXN1cD48bWk+eDwvbWk+PG1uPjI8L21uPjwvbXN1cD48bW8+KzwvbW8+PG1uPjQ8L21uPjxtaT54PC9taT48bWk+eTwvbWk+PC9tcm93PjwvbWZlbmNlZD48L21hdGg+SVC8UAAAAABJRU5ErkJggg==)
How can you use polynomial identities to factor polynomials and simplify numerical expressions ?
![27 x to the power of 9 minus 343 y to the power of 6](data:image/png;base64,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)
How can you use polynomial identities to factor polynomials and simplify numerical expressions ?
![27 x to the power of 9 minus 343 y to the power of 6](data:image/png;base64,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)
Use polynomial identities to multiply the expressions ?
![left parenthesis 10 plus 21 right parenthesis squared](data:image/png;base64,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)
Use polynomial identities to multiply the expressions ?
![left parenthesis 10 plus 21 right parenthesis squared](data:image/png;base64,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)
How is ( x + y )n obtained from (x + y)n-1
You could also get the value of from
by just multiplying a ( x + y) with
.
How is ( x + y )n obtained from (x + y)n-1
You could also get the value of from
by just multiplying a ( x + y) with
.
How can you use polynomial identities to factor polynomials and simplify numerical expressions ?
![m to the power of 8 minus 9 n to the power of 10](data:image/png;base64,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)
How can you use polynomial identities to factor polynomials and simplify numerical expressions ?
![m to the power of 8 minus 9 n to the power of 10](data:image/png;base64,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)
Use polynomial identities to multiply the expressions ?
![left parenthesis 7 plus 9 right parenthesis squared](data:image/png;base64,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)
Use polynomial identities to multiply the expressions ?
![left parenthesis 7 plus 9 right parenthesis squared](data:image/png;base64,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)
How can you use polynomial identities to factor polynomials and simplify numerical expressions ? 123 + 23
This can also be done by finding the cube of each values and adding them. But that might be time consuming. Hence, we use these identities.
How can you use polynomial identities to factor polynomials and simplify numerical expressions ? 123 + 23
This can also be done by finding the cube of each values and adding them. But that might be time consuming. Hence, we use these identities.
How can you use polynomial identities to factor polynomials and simplify numerical expressions ?
![open parentheses 11 cubed close parentheses plus 5 cubed](data:image/png;base64,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)
How can you use polynomial identities to factor polynomials and simplify numerical expressions ?
![open parentheses 11 cubed close parentheses plus 5 cubed](data:image/png;base64,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)
How can you use polynomial identities to factor polynomials and simplify numerical expressions ? ![27 x to the power of 9 minus 343 y to the power of 6](data:image/png;base64,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)
We use identities to speed up the process of multiplication and simplification. There are some basic polynomial identities that you need to by heart.
How can you use polynomial identities to factor polynomials and simplify numerical expressions ? ![27 x to the power of 9 minus 343 y to the power of 6](data:image/png;base64,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)
We use identities to speed up the process of multiplication and simplification. There are some basic polynomial identities that you need to by heart.
How can you use polynomial identities to factor polynomials and simplify numerical expressions ?
![x cubed minus 216](data:image/png;base64,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)
How can you use polynomial identities to factor polynomials and simplify numerical expressions ?
![x cubed minus 216](data:image/png;base64,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)
Use polynomial identities to multiply the expressions ?
103 × 97
Use polynomial identities to multiply the expressions ?
103 × 97
How can you use polynomial identities to factor polynomials and simplify numerical expressions ?
![open parentheses 9 m to the power of 4 close parentheses minus open parentheses 25 n to the power of 6 close parentheses](data:image/png;base64,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)
How can you use polynomial identities to factor polynomials and simplify numerical expressions ?
![open parentheses 9 m to the power of 4 close parentheses minus open parentheses 25 n to the power of 6 close parentheses](data:image/png;base64,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)
How can you use polynomial identities to factor polynomials and simplify numerical expressions ? ![m to the power of 8 minus 9 n to the power of 10](data:image/png;base64,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)
We use polynomial identities to reduce the time and space while solving polynomial expressions and equations.
How can you use polynomial identities to factor polynomials and simplify numerical expressions ? ![m to the power of 8 minus 9 n to the power of 10](data:image/png;base64,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)
We use polynomial identities to reduce the time and space while solving polynomial expressions and equations.