Question

What is the product of the polynomials below?
(6 - 5x^2)(x4-x^3)

Answer 1

-5x^6+5x^5+6x^4-6x^3

Explanation:

`\left(6-5x^2\right)\left(x^4-x^3\right)\\\\\mathrm{Apply\:FOIL\:method}:\\\quad \left(a+b\right)\left(c+d\right)=ac+ad+bc+bd\\\\a=6,\:b=-5x^2,\:c=x^4,\:d=-x^3\\\\=6x^4+6\left(-x^3\right)+\left(-5x^2\right)x^4+\left(-5x^2\right)\left(-x^3\right)\\\\\mathrm{Apply\:minus-plus\:rules}\\+\left(-a\right)=-a,\:\:\left(-a\right)\left(-b\right)=ab\\\\=6x^4-6x^3-5x^4x^2+5x^3x^2\\\\Simplify\\\\=-5x^6+5x^5+6x^4-6x^3`