Question
Use polynomial identities to factor the polynomials or simplify the expressions :
![x to the power of 8 minus 9](data:image/png;base64,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)
The correct answer is: Hence, the simplified expression is x^8 - 9 = (x^4 - 3)(x^4+3).
ANSWER:
Hint:
, where a and b can be real values, variables or multiples of both.
We are asked to simplify the given polynomial using identities.
Step 1 of 2:
The given expression is
. ![text It can be written as end text open parentheses x to the power of 4 close parentheses squared minus left parenthesis 3 right parenthesis squared text . This is of the form end text a squared minus b squared text where end text a equals x to the power of 4 straight & b equals 3 text , end text](data:image/png;base64,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)
Step 2 of 2:
Use the polynomial identity to simplify 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 x to the power of 8 minus 9 equals open parentheses x to the power of 4 close parentheses squared minus left parenthesis 3 right parenthesis squared end cell row cell equals open parentheses x to the power of 4 minus 3 close parentheses open parentheses x to the power of 4 plus 3 close parentheses space space space space end cell end table](data:image/png;base64,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)
Hence, the simplified expression is
.
Note:
The multiplication of algebraic expressions is a method of multiplying two given expressions consisting of variables and constants.
Related Questions to study
How is
obtained from ![left parenthesis x plus y right parenthesis to the power of n minus 1 end exponent](data:image/png;base64,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)
How is
obtained from ![left parenthesis x plus y right parenthesis to the power of n minus 1 end exponent](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAEwAAAASCAYAAADxEzisAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAPUJuPDwAAAeFJREFUeNpjYBgFuIAaENcC8QV8irKAuGOQeqAD6j56gcVAnAbE/3Ep0APi44M81o9C3YkObgCxDxCfAeJfQFxORTv/43OMwSAPMGMgPowmxgTEf6ApQhrqh3e0DjADaIANBXAYGnAwYA5NWTBgDcR7cXgcFyY5wLqAOIdGHvxPZfPy0MrZSCBeiMafT2v37wBiWyziyTgqgWaoHDUDbC4Qh2MRLwDiViS+JVoKmgTEGWj8ZFoH2CcgZsOh4RwQiyPxE4F4Cg1SWDw0pSMDLiC+BcTCSGJsUPfCwDog9kLib0Dj0yTA/uDR4AHEfVC2C47ygRoBBvLkKjSxemhbCB38QmKDCngOPHxKAgpnWfeHgObdQGwPbcQJk2ERMYUsyNwrSHxRIL6Lw/O/BrrmwZclYeXILxxtIGoW+t+Q2H1Qe9EBepYcELAbWh1jAyDxNVAPRNI4wEBNBiUovgttY6EDSzKKBaoDXM0KkMM3QQtfHmh7R5iGAQZqHvgB8VIgjsWhJgdL5UB3gK3hCipDtqEFkA+0RU2rACuANi8ukdBwHTBwHKmMYoNW19JY1C2H1py0AAHQAPYjoWs0YGAwdL79CLjhKJkVD81AxgAP72yDFuq4ytk0hlEABzpAvGWwOxIAhE5455JPXB8AAACwdEVYdE1hdGhNTAA8bWF0aCB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMTk5OC9NYXRoL01hdGhNTCI+PG1vPig8L21vPjxtaT54PC9taT48bW8+KzwvbW8+PG1pPnk8L21pPjxtc3VwPjxtbz4pPC9tbz48bXJvdz48bWk+bjwvbWk+PG1vPiYjeDIyMTI7PC9tbz48bW4+MTwvbW4+PC9tcm93PjwvbXN1cD48L21hdGg+8mttWgAAAABJRU5ErkJggg==)
Use Pascal triangle to expand (x + y)6
The expansion of the polynomial (x + y)6 can be found using the values of 6Cr
Use Pascal triangle to expand (x + y)6
The expansion of the polynomial (x + y)6 can be found using the values of 6Cr
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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)
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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)
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,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==)
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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)
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,iVBORw0KGgoAAAANSUhEUgAAADcAAAARCAYAAAB5LjRtAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAPUJuPDwAAAaJJREFUeNpjYBj64D8U/wLio0CsgkthFhB3DFJPdEDdhwswQeXPYZPUA+LjgzyWjkLdiQ/8wKXRAEt048LUBvZAfBjquG9AvAaIldDUGEPV4DPjILqgAdRzxIBQIJ5NZY+5AfEVIDaFJi8WIE4G4htALI6m9jDUk+hAEuoH9ABh6ALiHCIcIQ41nIOEzE4MOIPNUdCA7EITy8NSLqgB8RaoBzHADiC2JcIRm9CSLrU89wdPIYFeQFgC8V60GNsGxHy4DP8ExGwEHJABxLVkFNPEgLs4kpo8NP8hAzaoe2EA5DENckIO2ZKT0LxAC8+Bkt99aIHABMU+0Fj7hUX9LwIFH0meA5VAjiRUqOSUsiCP7YeWliC8ClohfyPgOYIAX7IMhUY9ua0HSgAHNMXgS5YEwW4gtsaRoW+QWIhQ03Og1NJMoEAhCHBVBQHYKkU6eq4ViKXRxHKwVA94Aa5KfDkQJ9LBc6CYCELKGtLQktkPi1pclThecBxLu+0lEAvSoc3oAi1M/kDz03IcbUhCzS+cYLg0nPFW1IO1ywPKZ2mkaAAAiPpuZM/W44UAAACIdEVYdE1hdGhNTAA8bWF0aCB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMTk5OC9NYXRoL01hdGhNTCI+PG1vPig8L21vPjxtbj43PC9tbj48bW8+KzwvbW8+PG1uPjk8L21uPjxtc3VwPjxtbz4pPC9tbz48bW4+MjwvbW4+PC9tc3VwPjwvbWF0aD6YBMINAAAAAElFTkSuQmCC)
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.