Home > CCA2 > Chapter 12 > Lesson 12.1.4 > Problem12-72

12-72.

Multiply the expressions in parts (a) through (d). Homework Help ✎

1. $(a + b)(a^2 - ab + b^2)$

Use a generic rectangle to help you. Pay attention to the negative sign.

$a^³ + b^³$

1. $(x - 2)(x^2 + 2x + 4)$

Use the same method as part (a).

1. $(y + 5)(y^2 - 5y + 25)$

Use the same method as part (a).

$x^³ − 8$

1. $(x - y)(x^2 + xy + y^2)$

Use the same method as part (b).

1. What did you notice about these products?

Look at your final answers. How many terms are there? And what is the largest exponent?

1. Make up another multiplication problem that will follow the same pattern.

The first factor is a binomial. The second factor is a trinomial. Look for a pattern in the terms of the trinomial. Match the sign pattern in one of the problems. Use a generic rectangle to multiply your factors to be sure you have the pattern.