Question

(x^2+2x-4)*(x^2+8x-9)

Answer 1

$(x^2+2x-4)(x^2+8x-9)=x^4+10x^3+3x^2-50x+36$

Solution:

Given expression is $(x^2+2x-4)(x^2+8x-9)$.

To find the product of two polynomials.

Multiply each term of first polynomial with the each term of the second polynomial.

$(x^2+2x-4)(x^2+8x-9)=x^2(x^2+8x-9)+2x(x^2+8x-9)-4(x^2+8x-9)$

                      $=(x^4+8x^3-9x^2)+(2x^3+16x^2-18x)+(-4x^2-32x+36)$

Removing the brackets and add all the terms.

                     $=x^4+8x^3-9x^2+2x^3+16x^2-18x-4x^2-32x+36$

Combine like terms together.

                     $=x^4+8x^3+2x^3-9x^2+16x^2-4x^2-18x-32x+36$

                     $=x^4+10x^3+3x^2-50x+36$

Hence $(x^2+2x-4)(x^2+8x-9)=x^4+10x^3+3x^2-50x+36$.