katelynn1998
17

# Which product will result in a sum or difference of cubes? (x + 7)(x2 – 7x + 14) (x + 8)(x2 + 8x + 64) (x – 9)(x2 + 9x + 81) (x – 10)(x2 – 10x + 100)

jayciejerrybob

$a^3+b^3=(a+b)(a^2-ab+b^2)\\\\a^3-b^3=(a-b)(a^2+ab+b^2)$ The first is wrong because   $14\not=7^2$ The second and the fourth are out because the signs are wrong. The third is the right answer:                                                           $(x-9)(x^2 + 9x + 81)= (x-9)(x^2 + 9\cdot x + 9^2)=x^3-9^3\\~ \qquad\qquad\qquad\qquad\qquad\qquad \left\{ a=x\atop\\b=9 \right\}$ Or:      $(x-9)(x^2 + 9x + 81)=x^3\ \underline{+\ 9x^2}\ \underline{\underline{+\ 81x}}\ \underline{-\ 9x^2}\ \underline{\underline{-\ 81x}}-9\cdot81=\\\\=x^3-9\cdot9^2=x^3-9^3$