Expanding the Product (3 - 2x)(2x + 7)(2x + 1)

In this article, we will explore the process of finding the expansions of the product (3 - 2x)(2x + 7)(2x + 1) step by step. This type of problem is commonly encountered in high school mathematics and is an important skill for students to master.

Step 1: Understand the problem

The goal is to find the expansions of the product (3 - 2x)(2x + 7)(2x + 1). This involves multiplying three binomials (expressions with two terms) together to obtain a polynomial expression with multiple terms.

Step 2: Expand the first factor

The first factor is (3 - 2x). To expand this, we can use the distributive property: (3 - 2x)(2x + 7) = 3(2x + 7) - 2x(2x + 7) = 6x + 21 - 4x^2 - 14x = -4x^2 - 8x + 21

Step 3: Expand the second factor

The second factor is (2x + 7). To expand this, we can use the distributive property: (-4x^2 - 8x + 21)(2x + 1) = -4x^2(2x + 1) - 8x(2x + 1) + 21(2x + 1) = -8x^3 - 4x^2 - 16x^2 - 8x + 42x + 21 = -8x^3 - 20x^2 + 34x + 21

Step 4: Combine the terms

Combining the terms, we get the final expansion: (3 - 2x)(2x + 7)(2x + 1) = -8x^3 - 20x^2 + 34x + 21

Therefore, the expansions of the product (3 - 2x)(2x + 7)(2x + 1) is -8x^3 - 20x^2 + 34x + 21.