# Express as a polynomial. (3x+2y)^{2}(3x-2y)^{2}

Express as a polynomial.
${\left(3x+2y\right)}^{2}{\left(3x-2y\right)}^{2}$
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Step 1
We know the identity that,
$\left(a-b\right)\left(a+b\right)={a}^{2}-{b}^{2}$...(1)
${\left(a-b\right)}^{2}={a}^{2}+{b}^{2}-2ab$...(2)
We have the given expression as
${\left(3x+2y\right)}^{2}{\left(3x-2y\right)}^{2}$
By using identity given by equation (1), we get value of expression as
${\left(3x+2y\right)}^{2}{\left(3x-2y\right)}^{2}={\left[\left(3x+2y\right)\left(3x-2y\right)\right]}^{2}$
$={\left[{\left(3x\right)}^{2}-{\left(2y\right)}^{2}\right]}^{2}$
$={\left(9{x}^{2}-4{y}^{2}\right)}^{2}$
Step 2
By using identity given by equation (2), we get value of expression as
${\left(3x+2y\right)}^{2}{\left(3x-2y\right)}^{2}={\left(9{x}^{2}-4{y}^{2}\right)}^{2}$
$={\left(9{x}^{2}\right)}^{2}+{\left(4{y}^{2}\right)}^{2}-2\left(9x\right)\left(4y\right)$
$=81{x}^{4}+16{y}^{4}-72{x}^{2}{y}^{2}$
Hence, expression ${\left(3x+2y\right)}^{2}{\left(3x-2y\right)}^{2}$ in polynomial form is represented as $81{x}^{4}+16{y}^{4}-72{x}^{2}{y}^{2}$.