# There are given the expressions: A= x^2+2x-2 and B= x^2-2x-4. Calculate A*B-A.

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A = x^2+2x-2 and B =x^2-2x-4.
To calculate A*B-A.
Therefore A*B-A = (x^2+2x-2)(x^2-2x-4)-(x^2+2x-2)....(1)
(x^2+2x-2)(x^2-2x-4)= (x^4-2x^3-4x^2)+(2x^3-4x^2-8x)+(-2x^2+4x+8)
=x^4+(-2+2)x^3+(-4-4-2)x^2+(-8+4)x+8=x^4+0*x^3-12x^2-4x+8. Therefore the right side in becomes:
x^4-10x^2-4x+8 -(x^2+2x-2)
=x^4-11x^2-6x+10 which is A*B-A

First, we'll notice that the expression which has to be calculated has as common factor the expression A.

E= A*B-A

E= A* (B-1)

Now, we'll put the values of the expressions A and B into the expression E.

E= (x^2+2x-2)*( x^2-2x-4-1)

E=x^2*( x^2-2x-5) +2x*( x^2-2x-5) -2*( x^2-2x-5)

E= x^4-2x^3-5x^2+2x^3-4x^2-10x-2x^2+4x+10

We'll group the terms which have the same power of the variable.

E= x^4 + (-2x^3+2x^3)+( -5x^2-4x^2-2x^2)+( -10x+4x) +10

**E= x^4 +0 -11x^2-6x+10**