Question

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

Answer 1

`=-10x^3+31x^2+12x+27`

Explanation:

Just take it 1 step at a time
`(2-x)(2-x)`
`a= x^2-4x+4`
`(x-3)(x-3)`
`b=x^2-6x+9`
`(x^2 +3)(x^2+3)`
`c=x^4 + 6x^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.
`(x^2 - 4x + 4)(x^2-6x+9)`
`=x^4-6x^3+9x^2`
`.........-4x^3+24x^2+36x`
`........................4x^2-24x+36`
`=x^4-10x^3+37x^2+12x+36`
all this subtracted to c
`=(x^4-10x^3+37x^2+12x+36)- (x^4 + 6x^2+9)`
distribute the minus
`=x^4-10x^3+37x^2+12x+36- x^4 - 6x^2-9`
combine and cancel what you can
`=-10x^3+31x^2+12x+27`