Question

Use the identity below to complete the tasks:

a3 - b3 = (a - b)(a2 + ab + b2)
When using the identity for the difference of two
cubes to factor 64x - 27
a. a=4, b=3
b.. a=3, b=4
c. a=2, b=3
d.. a=3, b=2

Answer 1

To factor the expression 64x^3 - 27, we identify the cube roots of each term as 4x and 3, respectively. Using the difference of two cubes identity, the factored form is (4x - 3)(16x^2 + 12x + 9).

Step-by-step explanation:

The student's question pertains to the factoring of the expression 64x^3 - 27 using the difference of two cubes identity, a^3 - b^3 = (a - b)(a^2 + ab + b^2). To factor this expression, we need to identify the cube root of each term, which gives us a = 4x and b = 3. Substituting these values into the identity, we get (4x - 3)(16x^2 + 12x + 9). Therefore, the factored form of 64x^3 - 27 using the given identity is (4x - 3)(16x^2 + 12x + 9).