Question

Use the factoring by special products method to factorize the expression.

a) a² −b²
b) a² +b²
c) a³ +b³
d) a³ -b³

Answer 1

Expressions a) and d) can be factored as (a + b)(a - b) and (a - b)(a² + ab + b²), respectively, while c) can be factored as (a + b)(a² - ab + b²). Expression b) is not factorizable using real numbers.

Step-by-step explanation:

The task is to factorize each given expression using the factoring by special products method. Here are the factorizations:

• a) a² − b² is a difference of squares and can be factored as (a + b)(a - b).
• b) a² + b² cannot be factored using real numbers as it does not represent a special product.
• c) a³ + b³ is a sum of cubes and can be factored as (a + b)(a² - ab + b²).
• d) a³ - b³ is a difference of cubes and can be factored as (a - b)(a² + ab + b²).