Question
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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)
The correct answer is: Polynomial identities are used to reduce the time and space while you solve higher degree polynomial expressions.
ANSWER:
Hint:
, where a and b can be real number, variables or multiples of them.
We are asked to find on how you could use a polynomial identity to multiply the given expression.
Step 1 of 2:
The given expression is:
.
Here,![a equals 3 x squared straight & b equals 5 y cubed](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAHoAAAATCAYAAABfohl2AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAQ3ZOC+gAAA0ZJREFUeNrtWF9kW1EYv6KqKkZUTO2hxMxM1ZiZmppSVVEzZaZmosYe9jDRlz1UzMyYPdTUjD3UzEyZycPMVSYqpmZMxOyhQs0eZqLkoaYiSvad+V0+Z+fcm3tu7m13mx8/ubn3OH++/9+xrHigDbaIm8ST1tEEl0OVOB3XgyaIt4kVq4fTxB9xP2Szp+e/Rt+I8wEvEctHXMlDxKfEhYPcxCTRJu7B82rEJ9hcUAwjR2c0308QSyyHnXWZaw9eEVVeVTHIfDcO2to2iHPEfvZOCHw94LyniO+hbB02YWgWCpUtzThRzH2NsIDqNo4RHxJvHcZwsxvQk20c0A0t5qUJeK0KV4hr/7GiXWsVcfD7xDoLbSMRHTaj8a6bxEeK9w/wzYGNKrOTaJLF83XiM824e8QlyOMXBLbhES3CVvQq8ZrifR7eK2OC+EU1kQh7K8QUlP4Glm2SWzrNMcdRMNSYAmRUMM7BAgoNr72oMEX8jmJNnLVPM06cfZt4l8lj2cPLTeXRqaJzxMfSu0HIbkjaQxOp8B9HncfhOF66CL/bBUjeZewMhOwoqmS4Zg7eudNBNSqEd0aR93ZDkkULc4vItEhMKsZlFToSkafgt0Aal96VIwjdKUSNz2iLdPiA71XD6vwqLDwFQa675DJd7h4ISdEORHQ5B8VtKVKROPc39j+NqDPgZxG5lRDPvwO0BX7bgySUrUMeVj9mKMQKBOMIdJu1VoNShX0Bhi9j3COadFMe05q7AG6Ayx6RUIkd6f9FK/prRN1tltjLWxxs3nDulmTIl5lh5RACeRp7oZhj0W+YDEEeH1G4ZmCsvvv8n1IIKEC4UWEMeVFVjb+D1yVRRZqE7iqqbLngugPv5XOuKHJ4P7x+OCJ5jEKRlqJuEkb62vRCRLQrz2EhI5jIDukQZeTMPqw3iUo4J41LYw9cCbPEVwZrCuE00J4ksLaoqPeR/zmKMLopdptWtMK7TiwiLSTAGSh5TpPCVoNe5izBygvw7rpHe2WKCbRyTdafzio8qAghy1iDMPwii4iwj3VL6JPb+HVQh2HUMLYakhx4oeis1YAOzrtc5LSxv64hbfVw2CAU/KknhvjDVrTBPcQMo0h5RvgDg7rupA9+x+oAAADgdEVYdE1hdGhNTAA8bWF0aCB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMTk5OC9NYXRoL01hdGhNTCI+PG1pPmE8L21pPjxtbz49PC9tbz48bW4+MzwvbW4+PG1zdXA+PG1pPng8L21pPjxtbj4yPC9tbj48L21zdXA+PG1pIG1hdGh2YXJpYW50PSJub3JtYWwiPiZhbXA7PC9taT48bWk+YjwvbWk+PG1vPj08L21vPjxtbj41PC9tbj48bXN1cD48bWk+eTwvbWk+PG1uPjM8L21uPjwvbXN1cD48L21hdGg+DuQt4wAAAABJRU5ErkJggg==)
Taking the values and the expression, it can be written as
.
Step 2 of 2:
Applying the identity for the expression
, we have:
![open parentheses 3 x squared plus 5 y cubed close parentheses open parentheses 3 x squared minus 5 y cubed close parentheses equals open parentheses 3 x squared close parentheses squared minus open parentheses 5 y cubed close parentheses squared](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAASQAAAAWCAYAAABpPOH+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAATRJrTQAAAA/NJREFUeNrtW9+HVVEU3q5cyYiMJD3ESHoYY0gPSRLJSK4xjPSQjBjJyNX76CExehg99NpDMiLpIeOKZGSMEWOM9JBI+gd6mIcxjsttLbMup23ve37tffba1/pY3HvOuefs7/vuWXvtffZRSiAQhEKPIoHYgDgjvAUCQWg0IB5AbAtvgUDABfvCW0q1vO3dgbguZe9QasnBjysQXyLnXcZXFrxjLNXOQfyRsneotQzlx0lKYmORcy/qayZvFHJJSlTrH+1v6vsS6SVa+tfSBUL6MYjfWYhVujlj51/E10zeExCbNRoWU4k6CvECYk7bvkG6iZb+tHQBDn6Y+OHN2IE46rk9dfAv4msu3vjDydT3q/SjPcr2PyGe04WrwmeJ2hsQVc53x7DvPMS6aOlVSxfg4IeJX4eGOb6h8w/taybvSWp0GmsQMxBN7biPFcXxXaL2PJwTM/lTiHnDvnUSXbR0r6ULcPJD5+cqIRTlH9rXTN7PIBZyXni3Yu9RtkTtBbyJBs3TPNTG5jFoqSLR0gU4+eGDXxn+7H3FnuFyjuOwDP1h2H7PcsEntM9Fieo6Ib2EuGXY3qZMrwP12TJsvwjxOTItVSRaugAnP3zwK8Ofva+7Wvmq4wRNVuFY+4blmG06ro85muTKmpMIlZDuUu+RxhHiOKq1d5+MPW04T1PrWWPQUkWiZd75rEH8OfnRrFiFlYGJPydfjejm/BO0B5xjCmKZPl/z0BMUSUgJCYC91iOIEcNx+Od7q217DLFYom1JZFqqSLR0AW5+JDV72I3R127G/mMQ0xBf1cEjTRs+0f4dVf2JRdkesY9DNJG2SKW4Xk5j+76nvh+H+AVx2FNCEi15JaRQfiQ1e9iN0dessraPETLOhjZd2Md6kipDElzOblqns5f6vJzRS9pQdMjGQUsViZZ1DNnq9IPLkI2Tr9bsfynnsbYVwfj7d9To28wSkq3d+DhyjAIzf6PEefUJuxi0VJFo6QKc/AgxqV2VfxBf8z4anaAJLR3Y2A804YU9zZZys8jMVUIaJzF1vIJoQawo86KuPFhQ/0/8xaClikRLF+Dkhw9+rviz8tW0eArLt1kaZ2JWxNWtv9XBzLvSxpUdzaSbEK8DJaT3lJEbFFMk9IylDMdHm98qtCvPwkhuWqpItHQBTn744FeGfxS+bmrjY1xTsEplHMYamaGPDZHcKcP53hDRujFLPR1O5uGLfviU4ILl2GlKdK2S17K97iBautPSBTj44ZNfUf5R+Fr3C4gc0KrImcvLtcOspQtw8MMnP5/8g/p6X9W/tD0kOlS6lh2bz4uWtWjpAiH9qIOfL/7cfR0ajFPZLhAtBUx8/QeqMTR7/PxZtAAAAmF0RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIj48bWZlbmNlZCBzZXBhcmF0b3JzPSJ8Ij48bXJvdz48bW4+MzwvbW4+PG1zdXA+PG1pPng8L21pPjxtbj4yPC9tbj48L21zdXA+PG1vPis8L21vPjxtbj41PC9tbj48bXN1cD48bWk+eTwvbWk+PG1uPjM8L21uPjwvbXN1cD48L21yb3c+PC9tZmVuY2VkPjxtZmVuY2VkIHNlcGFyYXRvcnM9InwiPjxtcm93Pjxtbj4zPC9tbj48bXN1cD48bWk+eDwvbWk+PG1uPjI8L21uPjwvbXN1cD48bW8+JiN4MjIxMjs8L21vPjxtbj41PC9tbj48bXN1cD48bWk+eTwvbWk+PG1uPjM8L21uPjwvbXN1cD48L21yb3c+PC9tZmVuY2VkPjxtbz49PC9tbz48bXN1cD48bWZlbmNlZCBzZXBhcmF0b3JzPSJ8Ij48bXJvdz48bW4+MzwvbW4+PG1zdXA+PG1pPng8L21pPjxtbj4yPC9tbj48L21zdXA+PC9tcm93PjwvbWZlbmNlZD48bW4+MjwvbW4+PC9tc3VwPjxtbz4mI3gyMjEyOzwvbW8+PG1zdXA+PG1mZW5jZWQgc2VwYXJhdG9ycz0ifCI+PG1yb3c+PG1uPjU8L21uPjxtc3VwPjxtaT55PC9taT48bW4+MzwvbW4+PC9tc3VwPjwvbXJvdz48L21mZW5jZWQ+PG1uPjI8L21uPjwvbXN1cD48L21hdGg+1uatFQAAAABJRU5ErkJggg==)
![equals 9 x to the power of 4 minus 25 y to the power of 6](data:image/png;base64,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)
Thus, the value is .![equals 9 x to the power of 4 minus 25 y to the power of 6](data:image/png;base64,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)
Note:
Polynomial identities are used to reduce the time and space while you solve higher degree polynomial expressions.
Related Questions to study
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,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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,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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,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)
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.
Use polynomial identities to multiply the expressions ?
![left parenthesis 2 x minus 5 right parenthesis left parenthesis 2 x plus 5 right parenthesis](data:image/png;base64,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)
Use polynomial identities to multiply the expressions ?
![left parenthesis 2 x minus 5 right parenthesis left parenthesis 2 x plus 5 right parenthesis](data:image/png;base64,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)
Use polynomial identities to multiply the expressions ?
![left parenthesis 3 straight x minus 7 right parenthesis squared](data:image/png;base64,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)
Use polynomial identities to multiply the expressions ?
![left parenthesis 3 straight x minus 7 right parenthesis squared](data:image/png;base64,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)
How can you use polynomial identities to multiply expressions ? 41
39
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
39
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 ?
![open parentheses 2 x squared plus y cubed close parentheses squared](data:image/png;base64,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)
Any expression of the form can be expanded using the identity
rather than using the conventional and time taking method of multiplying them,
.
How can you use polynomial identities to multiply expressions ?
![open parentheses 2 x squared plus y cubed close parentheses squared](data:image/png;base64,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)
Any expression of the form can be expanded using the identity
rather than using the conventional and time taking method of multiplying them,
.
Prove the difference of cubes identity : ![a cubed minus b cubed equals left parenthesis a minus b right parenthesis open parentheses a squared plus a b plus b squared close parentheses](data:image/png;base64,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)
To prove an equation to be equal, we have to prove either the RHS is equal to the LHS or vice versa. The side should be selected based on the simplification process.
Prove the difference of cubes identity : ![a cubed minus b cubed equals left parenthesis a minus b right parenthesis open parentheses a squared plus a b plus b squared close parentheses](data:image/png;base64,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)
To prove an equation to be equal, we have to prove either the RHS is equal to the LHS or vice versa. The side should be selected based on the simplification process.
Prove the sum of cubes identity : ![a cubed plus b cubed equals left parenthesis a plus b right parenthesis open parentheses a squared minus a b plus b squared close parentheses](data:image/png;base64,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)
To prove an equation to be equal, we have to prove either the RHS is equal to the LHS or vice versa. The side should be selected based on the simplification process.
Prove the sum of cubes identity : ![a cubed plus b cubed equals left parenthesis a plus b right parenthesis open parentheses a squared minus a b plus b squared close parentheses](data:image/png;base64,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)
To prove an equation to be equal, we have to prove either the RHS is equal to the LHS or vice versa. The side should be selected based on the simplification process.