Question 152236
Let's use a modified FOIL (First-Outer-Inner-Last) method to multiply"
{{{(highlight(x^8)+x^7)*(x^8+x^7-x^6) = (highlight(x^8)*x^8+highlight(x^8)*x^7-highlight(x^8)*x^6)+(x^7*x^8+x^7*x^7-x^7*x^6)}}} Now simplify this - remembering that when you multiply factors with the same base (x in this case) you will add the exponents of the factors.
{{{x^(8+8)+x^(8+7)-x^(8+6)+x^(7+8)+x^(7+7)-x^(7+6) = x^16+x^15-x^14+x^15+x^14-x^13}}} Now combine like-terms.
{{{x^16+2x^15-x^13}}} ...and this could be simplified to:
{{{x^13(x^3+2x^2-1)}}}