Maths-

General

Easy

Question

How can you use polynomial identities to multiply expressions ?
$open parentheses 2 x squared plus y cubed close parentheses squared$

hint Hint:

Let a and b be variables or real numbers, then: $left parenthesis a plus b right parenthesis squared equals a squared plus a b plus b squared$
We are asked to explain how you can use the polynomial identities to multiply expressions.

The correct answer is: 4x4 + 4x2y2 + y6

Step 1 of 2:
Here, the given expression is $open parentheses 2 x squared plus y cubed close parentheses squared$ , where $a equals 2 x squared straight & b equals y cubed$ .
So, we can use the identity $left parenthesis a plus b right parenthesis squared equals a squared plus a b plus b squared$ to find the expansion of $open parentheses 2 x squared plus y cubed close parentheses squared$
Step 2 of 2:
Apply the polynomial identity, $left parenthesis a plus b right parenthesis squared equals a squared plus a b plus b squared$ to get the answer of $open parentheses 2 x squared plus y cubed close parentheses squared$ .Thus, we have:
$table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell open parentheses 2 x squared plus y cubed close parentheses squared equals open parentheses 2 x squared close parentheses squared plus 2 space cross times space 2 x squared space cross times space y cubed space plus space open parentheses y cubed close parentheses squared end cell row cell equals 4 x to the power of 4 space plus space 4 x squared y cubed space plus space y to the power of 6 end cell end table$
Thus, the expansion is: $4 x to the power of 4 plus 4 x squared y cubed plus y to the power of 6$

Any expression of the form $left parenthesis a plus b right parenthesis squared$ can be expanded using the identity $left parenthesis a plus b right parenthesis squared equals a squared plus a b plus b squared$ rather than using the conventional and time taking method of multiplying them, $left parenthesis a plus b right parenthesis left parenthesis a plus b right parenthesis$ .

Prove the difference of cubes identity : $a cubed minus b cubed equals left parenthesis a minus b right parenthesis open parentheses a squared plus a b plus b squared close parentheses$

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.

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How can you use polynomial identities to multiply expressions ?

Let a and b be variables or real numbers, then: We are asked to explain how you can use the polynomial identities to multiply expressions.

The correct answer is: 4x4 + 4x2y2 + y6

Step 1 of 2:Here, the given expression is , where .So, we can use the identity to find the expansion of Step 2 of 2:Apply the polynomial identity, to get the answer of .Thus, we have:Thus, the expansion is:

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