Question

lou thinks the expression 27x^3-64 factors to (3x-4) (9x^2+12x+16). is he correct? How can you check his work? Show all work to justify your thinking.

Answer 1

Explanation:

(a³ - b³) = (a - b) (a² + ab + b²)

27x³ - 64 = 3³x³ - 4³

= (3x)³ - 4³ {a = 3x & b= 4)

Substitute in the above formula.

= (3x -4)([3x]² + 3x*4 + 4²)

= (3x - 4)(9x² + 12x + 16)

The expression 27x^3-64 factors to (3x-4) (9x^2+12x+16).