Express as a polynomial.

$(3x+2y)}^{2}{(3x-2y)}^{2$

midtlinjeg
2021-03-24
Answered

Express as a polynomial.

$(3x+2y)}^{2}{(3x-2y)}^{2$

You can still ask an expert for help

escumantsu

Answered 2021-03-26
Author has **98** answers

Step 1

We know the identity that,

$(a-b)(a+b)={a}^{2}-{b}^{2}$ ...(1)

${(a-b)}^{2}={a}^{2}+{b}^{2}-2ab$ ...(2)

We have the given expression as

$(3x+2y)}^{2}{(3x-2y)}^{2$

By using identity given by equation (1), we get value of expression as

$(3x+2y)}^{2}{(3x-2y)}^{2}={\left[(3x+2y)(3x-2y)\right]}^{2$

$={[{\left(3x\right)}^{2}-{\left(2y\right)}^{2}]}^{2}$

$={(9{x}^{2}-4{y}^{2})}^{2}$

Step 2

By using identity given by equation (2), we get value of expression as

$(3x+2y)}^{2}{(3x-2y)}^{2}={(9{x}^{2}-4{y}^{2})}^{2$

$={\left(9{x}^{2}\right)}^{2}+{\left(4{y}^{2}\right)}^{2}-2\left(9x\right)\left(4y\right)$

$=81{x}^{4}+16{y}^{4}-72{x}^{2}{y}^{2}$

Hence, expression$(3x+2y)}^{2}{(3x-2y)}^{2$ in polynomial form is represented as $81{x}^{4}+16{y}^{4}-72{x}^{2}{y}^{2}$ .

We know the identity that,

We have the given expression as

By using identity given by equation (1), we get value of expression as

Step 2

By using identity given by equation (2), we get value of expression as

Hence, expression

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