### Home > A2C > Chapter 13 > Lesson 13.1.4 > Problem13-76

13-76.

Parts (a) through (d) of problem 13-75 represent a general pattern known as the sum and difference of cubes. Use this pattern to factor each of the following polynomials.

1. $x^{3} + y^{3}$

See problem 13-75.

$\left(x + y\right)\left(x^{2} − xy + y^{2}\right)$

1. $x^{3} − 27$

See part (a).

1. $8x^{3} − y^{3}$

See part (a).

$\left(2x − y\right)\left(4x^{2} + 2xy + y^{2}\right)$

1. $x^{3} + 1$

See part (a).

1. Make up another problem involving the sum or difference of cubes and show how to factor it

Substitute values into the expression in part (a). Then factor as in part (a).