sums and differences of cubes?

Question

1. c^12+d^3
2. 1-a^6
3. 64-c^12
4. w^6-x^3y^9
5. 27k^2-k^5
6. 81w-24wx^3

Answer 1

1.)
c^12 + d^3 = (c^4 + d)(c^8 - c^4d + d^2)

2.)
1 - a^6 = (1 - a^2)(1 + a^2 + a^4) = (1 - a)(1 + a)(1 - a + a^2)(1 + a + a^2)

3.)
64 - c^12 = (4 + 2c^2 + c^4)(4 - 2c^2 + c^4)(2 - c^2)(2 + c^2)

4.)
w^6 - x^3y^9 = (w^2 - xy^3)(w^4 + w^2xy^3 + x^2y^6)

5.)
27k^2 - k^5 = k^2(27 - k^3) = k^2(3 - k)(9 + 3k + k^2)

6.)
81w - 24wx^3 = 3w(27 - 8x^3) = w(3 - 2x)(9 + 6x + 4x^2)

Answer 2

What's the question? Factor the expression?

Here's one. Only one problem per question please.

All sums and differences of cubes can factor.

a³ + b³ = (a + b)(a² - ab + b²)
a³ - b³ = (a - b)(a² + ab + b²)
____________

4) w^6 - x³y^9

w^6 - x³y^9 = (w²)³ - (xy³)³
= (w² - xy³)[(w²)² + w²xy³ + (xy³)²]
= (w² - xy³)[w^4 + w²xy³ + x²y^6]