What is the fully factored form of 32a³ + 12a²?
4a² (8a + 3), 4a (8a² + 3a), 12a² (3a + 1), 12a (3a² + a)

Solution:

Given: the algebraic expression 32a³ + 12a²

Factorization of algebraic expression can be factored in by using the algebraic identity or regrouping the terms or taking the common factors out.

Since the two terms of the algebraic expression have variables of unequal degrees the simplest form of factorization is carried out by taking the highest common factor out of the brackets.

4 is the GCF of 32 and 12.

a²  is the GCF of a³ and a².

Taking out 4a² as the common factor, we get

32a³ + 12a² = 4a²(8a + 3)

What is the fully factored form of 32a³ + 12a²?
4a² (8a + 3), 4a (8a² + 3a), 12a² (3a + 1), 12a (3a² + a))

Summary:

The fully factored form of the given algebraic expression is 4a²(8a + 3).