# How do you simplify (2- x ) ^ { 2} ( x - 3) ^ { 2} - ( x ^ { 2} + 3) ^ { 2}?

Mar 20, 2018

$= - 10 {x}^{3} + 31 {x}^{2} + 12 x + 27$

#### Explanation:

Just take it 1 step at a time
$\left(2 - x\right) \left(2 - x\right)$
$a = {x}^{2} - 4 x + 4$
$\left(x - 3\right) \left(x - 3\right)$
$b = {x}^{2} - 6 x + 9$
$\left({x}^{2} + 3\right) \left({x}^{2} + 3\right)$
$c = {x}^{4} + 6 {x}^{2} + 9$
you'll have to distribute a and b so simply take the x^2 and multiply it to every term in b, then take -4x and multiply it to every term in b and so on.
$\left({x}^{2} - 4 x + 4\right) \left({x}^{2} - 6 x + 9\right)$
$= {x}^{4} - 6 {x}^{3} + 9 {x}^{2}$
$\ldots \ldots \ldots - 4 {x}^{3} + 24 {x}^{2} + 36 x$
$\ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots 4 {x}^{2} - 24 x + 36$
$= {x}^{4} - 10 {x}^{3} + 37 {x}^{2} + 12 x + 36$
all this subtracted to c
$= \left({x}^{4} - 10 {x}^{3} + 37 {x}^{2} + 12 x + 36\right) - \left({x}^{4} + 6 {x}^{2} + 9\right)$
distribute the minus
$= {x}^{4} - 10 {x}^{3} + 37 {x}^{2} + 12 x + 36 - {x}^{4} - 6 {x}^{2} - 9$
combine and cancel what you can
$= - 10 {x}^{3} + 31 {x}^{2} + 12 x + 27$