Question

On

17. Find the product.
(x – 3)(x + 3)(2x - 1)
Ø 2x3 + 13x2 – 24x + 9
B 2x3 – 11x2 – 24x + 9
© 2x3 – x2 – 18x + 9
D 2x3 + 9
ent.

Answer 1

C

Explanation:

Given

(x - 3)(x + 3)(2x - 1)

Expand (x - 3)(x + 3) = x² - 9 ← difference of squares factors, thus

= (x² - 9)(2x - 1)

Each term in the second factor is multiplied by each term in the first factor, that is

= x²(2x - 1) - 9(2x - 1) ← distribute both parenthesis

= 2x³ - x² - 18x + 9 → C

Answer 2

`\large\boxed{C.\ 2x^3-x^2-18x+9}`

Explanation:

`\text{Use}\ a^2-b^2=(a-b)(a+b)\qquad(*)\\\\\underbrace{(x-3)(x+3)}_((*))(2x-1)=(x^2-3^2)(2x-1)=(x^2-9)(2x-1)\\\\\text{Use FOIL:}\ (a+b)(c+d)=ac+ad+bc+bd\\\\=(x^2)(2x)+(x^2)(-1)+(-9)(2x)+(-9)(-1)\\\\=2x^3-x^2-18x+9`