Question
Use polynomial identities to multiply the expressions ?
![left parenthesis 7 plus 9 right parenthesis squared](data:image/png;base64,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)
The correct answer is: Thus, the product is (7+9)^2=256
ANSWER:
Hint:
, where x and a can be real values, variables or multiples of both.
We are asked to use polynomial identities to multiply the expression.
Step 1 of 2:
The given expression is ![left parenthesis 7 plus 9 right parenthesis squared text . This is of the form end text left parenthesis a plus b right parenthesis squared text where end text a equals 7 straight & b equals 9 text . end text](data:image/png;base64,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)
Step 2 of 2:
Use the identity to get 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 left parenthesis 7 plus 9 right parenthesis squared equals 7 squared plus 2 left parenthesis 7 right parenthesis left parenthesis 9 right parenthesis plus 9 squared end cell row cell equals 49 plus 126 plus 81 space space space space space space space space space space space space space space space space space space end cell row cell equals 256 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 ![left parenthesis 7 plus 9 right parenthesis squared equals 256](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 ? 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,iVBORw0KGgoAAAANSUhEUgAAAEkAAAASCAYAAAAXOvPoAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAQ3ZOC+gAAAXhJREFUeNpjYKAf+A/Fv4D4AhC7MQwuMOjcpwHEDxkGL8Drviwg7qCDI5iA+B0SvwNq92AB6O6DAz0gPk4HBwgD8RQgTkQTPwp1w0ADXO6DO9IAi7gaENdC8yk+QIw6WL6PxSJnDMSHaVjWYMOkuA8cOEdxWLIYiNNwGEqOOj4gboWqRQeHoYFF7UAiBeB0XxcQ51DJMmLV/cAilkdCmfifRoGE0307gNiWjo4C2XUGi7glEO8dBIGE1X2fgJiNxo6C5fcf0EiRx6KGDeqWgQgkgu77MwiSNwz8ooHnf0EDfxsQFwExDzkOGwqB9J8IjA+wQCsFUA18A9pgJAnQI7sRA2iR3bABUJfjIKmadgOx9SAIJFoU3KTUrnjBQDQBsIEcqFtobY8OEN8lVRO+xiQ9A4mUxiSx9qyDplAmKPaABlAQOQ48jqPvRGwBSWpBSq9uSSgQ34JWTqBO6yogNiXXMHp1cHGBwdLBJQgy6DRUgq1MTBusgQIAwOyNEZXWtOkAAACudEVYdE1hdGhNTAA8bWF0aCB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMTk5OC9NYXRoL01hdGhNTCI+PG1mZW5jZWQgc2VwYXJhdG9ycz0ifCI+PG1zdXA+PG1uPjExPC9tbj48bW4+MzwvbW4+PC9tc3VwPjwvbWZlbmNlZD48bW8+KzwvbW8+PG1zdXA+PG1uPjU8L21uPjxtbj4zPC9tbj48L21zdXA+PC9tYXRoPvS5qBIAAAAASUVORK5CYII=)
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,iVBORw0KGgoAAAANSUhEUgAAAGcAAAATCAYAAACN8hMuAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAQ3ZOC+gAAAtZJREFUeNrtV89nXFEUfkaMGmMYY8wiizC6qIqRXVVFlaqqiChRFVXRTRddzD9QXVSpLkYX3VR0UVUhoioiSlWMqBoqKqoqVHUZ3c2iniqv3+Ebruu+d++78zJ5zHx85v2478y995z7nXOCIB9YAr+BB+ByMH44B3bBEIzIXECc8QycAuvgNnh9jBxzFtwHZ/M4uX06ZoBpcG+MnPMSnM/r5ETKSsp9AfwzRs75Da6Av8BDk6xfADfBPvgX/MIPdEQW+uASuAYWwQr4nHPIEvIfO3R6yE14CtYs3y3ErMvXngn/uP4K90CuV9UBkoxugmVFBz/ymWveWBuyIPjB6LnB3yyxyzxWVJ7Nge8SvimzSIkysheHQ6qF+r/W9c9QcmxoMEecymgjF1ggjAL9hHdygu+kVIS+xxwkqKvKvTj8s8uHocOYLUaNDlnYY8Pzh3xnwkVK6vQIHNMEv8e8E5n/oEi5r70XVAIdbfARr1ssCiosjCQwr9r+7DylLQl3wfuWSqyh3K8aTsUgX0kgvAVPH7NTGpyHyMk1w/siFWPG0TlJ9m6DT7RnJY5V89MKZf3Ipc8TieoxgpJkr6eVwTokAjq8vqxE40lAL17aMePktN/TvvO1J87a0J49sAR0IqqM4CuWcV1WLTa8V+SqlvEG+1SMVRYgPc5LRcugFtEQ9mS9X5X7Ok+IV35uOkrLMktJF7RZGrdy1l+UuaEqeoa1R0PYC7SerZNwYhNxhpVDyTKuwMQ352Bz0D91UpTlo0SYcR9nKqD2GPRNnpqCT5LcsOQPtSfpOp7CLTq7zPKwliPHtJiYXaR0GHtSiS2Cr8FbPhPd5slxwbrewRpQp+zVtP7l1Qk5okspnmLkSq78yWrKxzlp7LVZUh/4Tj7NUT7SmiZTKfompldZd6nhjwHzDMCQ3GWwBJ7OSWNviTYWgwlyB3HKp8k25BM7bOgnyBlmKX9e+A9wYcgrXYZkCgAAAKl0RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIj48bW4+Mjc8L21uPjxtc3VwPjxtaT54PC9taT48bW4+OTwvbW4+PC9tc3VwPjxtbz4mI3gyMjEyOzwvbW8+PG1uPjM0MzwvbW4+PG1zdXA+PG1pPnk8L21pPjxtbj42PC9tbj48L21zdXA+PC9tYXRoPrnffCsAAAAASUVORK5CYII=)
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,iVBORw0KGgoAAAANSUhEUgAAAGcAAAATCAYAAACN8hMuAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAQ3ZOC+gAAAtZJREFUeNrtV89nXFEUfkaMGmMYY8wiizC6qIqRXVVFlaqqiChRFVXRTRddzD9QXVSpLkYX3VR0UVUhoioiSlWMqBoqKqoqVHUZ3c2iniqv3+Ebruu+d++78zJ5zHx85v2478y995z7nXOCIB9YAr+BB+ByMH44B3bBEIzIXECc8QycAuvgNnh9jBxzFtwHZ/M4uX06ZoBpcG+MnPMSnM/r5ETKSsp9AfwzRs75Da6Av8BDk6xfADfBPvgX/MIPdEQW+uASuAYWwQr4nHPIEvIfO3R6yE14CtYs3y3ErMvXngn/uP4K90CuV9UBkoxugmVFBz/ymWveWBuyIPjB6LnB3yyxyzxWVJ7Nge8SvimzSIkysheHQ6qF+r/W9c9QcmxoMEecymgjF1ggjAL9hHdygu+kVIS+xxwkqKvKvTj8s8uHocOYLUaNDlnYY8Pzh3xnwkVK6vQIHNMEv8e8E5n/oEi5r70XVAIdbfARr1ssCiosjCQwr9r+7DylLQl3wfuWSqyh3K8aTsUgX0kgvAVPH7NTGpyHyMk1w/siFWPG0TlJ9m6DT7RnJY5V89MKZf3Ipc8TieoxgpJkr6eVwTokAjq8vqxE40lAL17aMePktN/TvvO1J87a0J49sAR0IqqM4CuWcV1WLTa8V+SqlvEG+1SMVRYgPc5LRcugFtEQ9mS9X5X7Ok+IV35uOkrLMktJF7RZGrdy1l+UuaEqeoa1R0PYC7SerZNwYhNxhpVDyTKuwMQ352Bz0D91UpTlo0SYcR9nKqD2GPRNnpqCT5LcsOQPtSfpOp7CLTq7zPKwliPHtJiYXaR0GHtSiS2Cr8FbPhPd5slxwbrewRpQp+zVtP7l1Qk5okspnmLkSq78yWrKxzlp7LVZUh/4Tj7NUT7SmiZTKfompldZd6nhjwHzDMCQ3GWwBJ7OSWNviTYWgwlyB3HKp8k25BM7bOgnyBlmKX9e+A9wYcgrXYZkCgAAAKl0RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIj48bW4+Mjc8L21uPjxtc3VwPjxtaT54PC9taT48bW4+OTwvbW4+PC9tc3VwPjxtbz4mI3gyMjEyOzwvbW8+PG1uPjM0MzwvbW4+PG1zdXA+PG1pPnk8L21pPjxtbj42PC9tbj48L21zdXA+PC9tYXRoPrnffCsAAAAASUVORK5CYII=)
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,iVBORw0KGgoAAAANSUhEUgAAAEIAAAARCAYAAABpTnqxAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAQ3ZOC+gAAAbFJREFUeNpjYCAd/IfiX0B8AYjdGEYBgwYQPxwNBgYGJiB+N9IDQRiIpwBx4kgOBFg5EUsj862BeA0Qf0Iqi6LxqFcD4lqoOnzAFIhXQc39AcSbgNieUsfyAXErEKfRICAOAnEkEPNA+VpAfBQqhg0shrrjPx4z06AeV0NyPyhwD1PL0T/olArlgfgSESkVGwAF5BliLUoG4g4s4s1QOWzAlhQL6BDouAJiJp7UhBWcA2JxJH4itEDEVj6AHLUDGlP0AJbQ7EFOQNwAYklSLPMA4j4o2wWI9w6SwpkDiE9CC1FyAuIHtGxYB8TfoAXwGQIFMMNuaEl6AVpFUqN2wYcJAUEg3kBkC/Y/HnFQavcCYhZo+wcUqLeAOAuXYQXQENMbBClBCRoIKiQEPDYAqi6lsYgbAPFTfPV3H6mFC42a77OBmIvEFIgNbIOmAmzgF7bQ3wS1mAeah4QHKBDEoQ0fFjKyIjYASv7hOAL7JLKAKDTUkD3uA22oDATYAnUkA5UCgg3aSEtGClxzaLvEBVnROhx5aDm0JhmoJjyxhSsx6kShWe0LEP+BBoztaL8ZDQAAWQttjRgWwXQAAAB9dEVYdE1hdGhNTAA8bWF0aCB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMTk5OC9NYXRoL01hdGhNTCI+PG1zdXA+PG1pPng8L21pPjxtbj4zPC9tbj48L21zdXA+PG1vPiYjeDIyMTI7PC9tbz48bW4+MjE2PC9tbj48L21hdGg+XmTPWQAAAABJRU5ErkJggg==)
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.
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.