Key to "Express as a polynomial. (3x+2y)2(3x−2y)2"

midtlinjeg

Answered question

2021-03-24

Express as a polynomial.

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

escumantsu

Skilled2021-03-26Added 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} - 2 a b

...(2)
We have the given expression as

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

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

{(3 x + 2 y)}^{2} {(3 x - 2 y)}^{2} = {[(3 x + 2 y) (3 x - 2 y)]}^{2}

= {[{(3 x)}^{2} - {(2 y)}^{2}]}^{2}

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

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

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

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

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

Hence, expression

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

in polynomial form is represented as

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

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