Question
Use polynomial identities to multiply the expressions ?
103 × 97
The correct answer is: Thus, the product is 103 × 97 = 9991
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 ![103 cross times 97 text . It can be written as end text 103 cross times 97 equals left parenthesis 100 plus 3 right parenthesis left parenthesis 100 minus 3 right parenthesis text . end text](data:image/png;base64,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)
![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 100 straight & b equals 3 text . end text](data:image/png;base64,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)
Step 2 of 2:
Applying the identity on the expression, we get:
![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 103 cross times 97 equals left parenthesis 100 plus 3 right parenthesis left parenthesis 100 minus 3 right parenthesis end cell row cell equals 100 squared minus 3 squared 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 row cell equals 10 comma 000 minus 9 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 row cell equals 9991 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,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)
Thus, the product is 103 × 97 = 9991
Note:
The multiplication of algebraic expressions is a method of multiplying two given expressions consisting of variables and constants.
Related Questions to study
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.
Use polynomial identities to multiply the expressions ?
18 × 22
Use polynomial identities to multiply the expressions ?
18 × 22
Use polynomial identities to multiply the expressions;
![left parenthesis 12 plus 15 right parenthesis squared](data:image/png;base64,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)
Use polynomial identities to multiply the expressions;
![left parenthesis 12 plus 15 right parenthesis squared](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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)
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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)
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.
Use polynomial identities to multiply the expressions ?
![open parentheses 6 minus y cubed close parentheses squared](data:image/png;base64,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)
Use polynomial identities to multiply the expressions ?
![open parentheses 6 minus y cubed close parentheses squared](data:image/png;base64,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)
Use polynomial identities to multiply the expressions;
![open parentheses 3 x squared plus 5 y cubed close parentheses open parentheses 3 x squared minus 5 y cubed close parentheses](data:image/png;base64,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)
Use polynomial identities to multiply the expressions;
![open parentheses 3 x squared plus 5 y cubed close parentheses open parentheses 3 x squared minus 5 y cubed close parentheses](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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)
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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)
We use identities to speed up the process of multiplication and simplification. There are some basic polynomial identities that you need to by heart.
Use polynomial identities to multiply the expressions ?
![open parentheses 8 minus x squared close parentheses open parentheses 8 plus x squared close parentheses](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAHAAAAASCAYAAACD3FoaAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAQ3ZOC+gAAAgxJREFUeNrtmb9Lw0AcxY8iGURcREQcBBERh1JwEhEpODg4iODgKIIUKeL/IEIRcSiuTiIu4iAigohIKUUQcXJzcnAXBwnC+b3wquG4S1qTK5fEBw/S/Djy4S7fe3dlLHnisEuuk0dZupR2vh/lyBvkx3++X4kHKgkD/fQdV8CQSb48uZEwuFnynXSuDpas8XkXCtK5bnKV/IGRcEUesgRuEO88Ip2fJNeyxlfAzbIOyTvkLrKDT/jeArgx8gUgVaoBNCt8bJdcDqm/zYnVtWBkXpJ7A+7ZlOY6U3zcEj6vdMwobhSlpUcCfDXUMWuagLGNa00JuPGQtqbINx3g45bwsXeUEFlV9Lb/wT2DX5eIzAO+36vkA806yW9ZDphM83FL+NhXQDJ1YZGG3jQjOS7Nk/dxPCePsjbldoCPW8KnBBwmH6MmO74E9KKLsZrREzaaZF0jPj+R+wx2YJr4lCXmTANSJN8a/Aq38HL5CG20UkLj4OOW8HmjYjokobV6LYrEO5yizKxEaEee5E3xcUv4lDH7mak3UicwV8QtsWA9x+JaJMOHCCWmDCbTfNwSPuVCdwmQRcTrHI7FHFGKufP6EZ/9QAvkoz+218pCPg4+bgmfp4aiLi8j+rooKyKpLcbceQ7mI9UW1gmSWzvSbaWlnS+Rm70qpWkzux0+TyWWvL9b5Ll8PeB66vi+AWRU1CN+6EEsAAABDnRFWHRNYXRoTUwAPG1hdGggeG1sbnM9Imh0dHA6Ly93d3cudzMub3JnLzE5OTgvTWF0aC9NYXRoTUwiPjxtZmVuY2VkIHNlcGFyYXRvcnM9InwiPjxtcm93Pjxtbj44PC9tbj48bW8+JiN4MjIxMjs8L21vPjxtc3VwPjxtaT54PC9taT48bW4+MjwvbW4+PC9tc3VwPjwvbXJvdz48L21mZW5jZWQ+PG1mZW5jZWQgc2VwYXJhdG9ycz0ifCI+PG1yb3c+PG1uPjg8L21uPjxtbz4rPC9tbz48bXN1cD48bWk+eDwvbWk+PG1uPjI8L21uPjwvbXN1cD48L21yb3c+PC9tZmVuY2VkPjwvbWF0aD5UXVHeAAAAAElFTkSuQmCC)
Use polynomial identities to multiply the expressions ?
![open parentheses 8 minus x squared close parentheses open parentheses 8 plus x squared close parentheses](data:image/png;base64,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)
Use polynomial identities to multiply the expressions ?
![open parentheses x squared plus y to the power of 6 close parentheses squared](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAEcAAAAWCAYAAACSYoFNAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAATRJrTQAAAAi1JREFUeNrtWM9HRFEYfUaSjMhI0i5JMjK0SJI2LZKMNkmSjEgy0j+QFom0aNUuLUYSSYtkRFpkjNkkSauhRcu0m0UyYvo+znDd7n3v3fdjJmMOh/fuj3fvPe/c77vvWVYTFbBMzBP7m5L8RYS4QXxqSqHHdyNbc5T4gEVW5+UWk+jbkNYcwthxD3178GL7dA14Yfv/0ZoukSFOaOr2sT4VBog3EEiJYWIhgAmGak0HfBKXiO/EInFeqs9jnbJjssQOuwdzx4TPyTlaM2T8EI+x0FZcp4T6EWJO6sPCDNo9NIFF+YGjNWuAIuJeFVG4SEQOIsnJpKIL4AfEtE/HOFrTJtMFBXZKp3DP7nmU2myaxtVbTSBb1TxoF3WurRmAOCfEBUX5FnFPiJsZvKQW4hFxWmo/Rrw3mWAJKqvAqbFbuE9hUMvEmgGIswKHi2jHVooJZRyQ34gfioBcdVPJNJDpwMof4nrKVPUAxZkhXkhlO8RtD2OWgxKHcYcU/Sy9JT+naTuqwOO+CvddcEhb2OLYbavqvi4rzgi1dA7jS7g+xLxMYbyt2Bnjmjouv8RkFussTg5nqD64JuJhPOOArEvlPIlrBL4o0mKsjuJwJkoSz4jLHsdLKwK7ZXoI7EKKFsWYJZ7WUZwtpPQXH+PJh0BXKAgxhfflFbFX0e5ccXaoFeYgZtJjf9XngysE9eEZJpI+55j3k1TWA/plERayCKhewHFmzWpQxPFhWzP8AuJPhmhWl15iAAAA0XRFWHRNYXRoTUwAPG1hdGggeG1sbnM9Imh0dHA6Ly93d3cudzMub3JnLzE5OTgvTWF0aC9NYXRoTUwiPjxtc3VwPjxtZmVuY2VkIHNlcGFyYXRvcnM9InwiPjxtcm93Pjxtc3VwPjxtaT54PC9taT48bW4+MjwvbW4+PC9tc3VwPjxtbz4rPC9tbz48bXN1cD48bWk+eTwvbWk+PG1uPjY8L21uPjwvbXN1cD48L21yb3c+PC9tZmVuY2VkPjxtbj4yPC9tbj48L21zdXA+PC9tYXRoPmEJ3iUAAAAASUVORK5CYII=)
Use polynomial identities to multiply the expressions ?
![open parentheses x squared plus y to the power of 6 close parentheses squared](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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)
Factorization of polynomial of higher degree can be done by polynomial identities. This is used to reduce time and space.
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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)
Factorization of polynomial of higher degree can be done by polynomial identities. This is used to reduce time and space.
Use polynomial identities to multiply the expressions ?
![open parentheses 4 straight x squared plus 6 straight y squared close parentheses open parentheses 4 straight x squared minus 6 straight y squared close parentheses](data:image/png;base64,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)
Use polynomial identities to multiply the expressions ?
![open parentheses 4 straight x squared plus 6 straight y squared close parentheses open parentheses 4 straight x squared minus 6 straight y squared close parentheses](data:image/png;base64,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)
Use polynomial identities to multiply the expressions; ![left parenthesis 12 plus 15 right parenthesis squared](data:image/png;base64,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)
Polynomial identities are used to reduce the time and space while you solve higher degree polynomial expressions.
Use polynomial identities to multiply the expressions; ![left parenthesis 12 plus 15 right parenthesis squared](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAEsAAAARCAYAAACVW1F7AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAPUJuPDwAAAa9JREFUeNpjYBgF6OA/FP8C4qNArIJLYRYQd4yQQOmA+hcXYILKn8MmqQfEx0dYKjoK9Tc+8AOXRgMs4mpAXAvEF3AYZg3Ea4D4EzTpgtRF09iThNz0Hw9GBsZAfBiPPfZAfBBd0AAaWNjAYiBOw2IRDIAMiwRiHihfC2pWJA0Di5Cb/pNg1mFooKEDSag/lNAluoA4h4iCj1ggD8SXSCxUyS2MKTUvD0s5DUq5W6ABhgF2ALEtlT30Y4gEliUQ70VLUduAmA+XBlB5w0ZFD1niydaDLbDYoP6HAVBAaeDT8IeKHuIA4pPQgn8gA+sXNBBAni9CKlOxgV8EKgeaBJYgEG8AYjciG37E1lrkuokFWniDas4beFLML1JiiBrZUAkaUCpUTCHU1OeGrRmAJRsSBLuJyDb4HAaKsdlAzEUHT1O70kEv4AkCSpoO4kC8CprkGQZxYOkA8V0s4jlQ/xMNDIiovXA5bAuh2mMAAmsdNMUwQbEHNKCCSGiU4gXHcfSTCBW+lBbSlIwM4LIrFIhvQSuud9CUb4rFHELdHZxgtCNNIsgYQUM0XdD+JdEAADnnki5pzrVeAAAAinRFWHRNYXRoTUwAPG1hdGggeG1sbnM9Imh0dHA6Ly93d3cudzMub3JnLzE5OTgvTWF0aC9NYXRoTUwiPjxtbz4oPC9tbz48bW4+MTI8L21uPjxtbz4rPC9tbz48bW4+MTU8L21uPjxtc3VwPjxtbz4pPC9tbz48bW4+MjwvbW4+PC9tc3VwPjwvbWF0aD4QHzEjAAAAAElFTkSuQmCC)
Polynomial identities are used to reduce the time and space while you solve higher degree polynomial expressions.
How can you use polynomial identities to multiply expressions ?
![41 cross times 39](data:image/png;base64,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)
How can you use polynomial identities to multiply expressions ?
![41 cross times 39](data:image/png;base64,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)
Use polynomial identities to multiply the expressions; ![open parentheses 3 x squared plus 5 y cubed close parentheses open parentheses 3 x squared minus 5 y cubed close parentheses](data:image/png;base64,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)
Polynomial identities are used to reduce the time and space while you solve higher degree polynomial expressions.
Use polynomial identities to multiply the expressions; ![open parentheses 3 x squared plus 5 y cubed close parentheses open parentheses 3 x squared minus 5 y cubed close parentheses](data:image/png;base64,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)
Polynomial identities are used to reduce the time and space while you solve higher degree polynomial expressions.