Question

32. Multiply or find the special product (x-3) a. - 9x +27x+27 b. x-9x®-27x-27 c. X-9x +27x-27 d. x +9x +27x+27 e. +9x°-27x+27 33. Find the product. The expression is not polynomial, but the formula can still be used.) (3+ *)(3-6) a. 3-X b. 9+x c. d. e. 1-9 9-X 3+x 34. Completely factor the difference of two squares. - 16 a. (x+4)-(-4) b. (x+4) c. (x+4)(x-4) d. (x+4)+(x-4) c. (x-4) 35. Factor the perfect square trinomial. -16x + 64 a. (x+3)(8 - x) b. (x+8) c. (x-8) d. (x+8)x-8) e. (x-8)(x-8) 36. Completely factor the expression. brx-4) c. 2(x+4) c. x'(x-3)

Answer 1

32. (x - 3)³

= (x - 3)(x - 3)²

= (x - 3)(x² - 6x + 9)

= x³ - 6x² + 9x - 3x² + 18x - 27

= x³ - 9x² + 27x - 27

33. (3 + $\sqrt{x}$)(3 - $\sqrt{x}$)

= (3)² - ($\sqrt{x}$)² [Since a² - b² = (a + b)(a - b)]

= 9 - x

34. x² - 16

= x² - (4)²

= (x + 4)(x - 4) [Since a² - b² = (a + b)(a - b)]

35. x² - 16x + 64

= x² - 2(8)x + (8)²

= (x - 8)² [Since (a - b)² = a² - 2ab + b²]

36. x⁴ - 4x³

= x³ (x - 4)