How do you simplify (2- x ) ^ { 2} ( x - 3) ^ { 2} - ( x ^ { 2} + 3) ^ { 2}(2−x)2(x−3)2−(x2+3)2?

1 Answer
Reynaldo G.
Mar 20, 2018

=-10x^3+31x^2+12x+27=−10x3+31x2+12x+27

Explanation:

Just take it 1 step at a time
(2-x)(2-x)(2−x)(2−x)
a= x^2-4x+4a=x2−4x+4
(x-3)(x-3)(x−3)(x−3)
b=x^2-6x+9b=x2−6x+9
(x^2 +3)(x^2+3)(x2+3)(x2+3)
c=x^4 + 6x^2+9c=x4+6x2+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)(x2−4x+4)(x2−6x+9)
=x^4-6x^3+9x^2=x4−6x3+9x2
.........-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

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