(x2 + 4x + 8)(2x - 1)

3 min read Jun 17, 2024

Expanding the Expression (x² + 4x + 8)(2x - 1)

This article will guide you through the process of expanding the expression (x² + 4x + 8)(2x - 1). We will utilize the distributive property, also known as the FOIL method, to achieve this.

Understanding the Distributive Property

The distributive property states that multiplying a sum by a number is the same as multiplying each addend individually by that number and then adding the products. In simpler terms, we can distribute the multiplication over the addition.

Applying the FOIL Method

The FOIL method is a mnemonic device for remembering the order of multiplication when expanding two binomials. FOIL stands for:

First: Multiply the first terms of each binomial.
Outer: Multiply the outer terms of the binomials.
Inner: Multiply the inner terms of the binomials.
Last: Multiply the last terms of each binomial.

Let's apply the FOIL method to our expression:

First: (x²) * (2x) = 2x³
Outer: (x²) * (-1) = -x²
Inner: (4x) * (2x) = 8x²
Last: (4x) * (-1) = -4x
Inner: (8) * (2x) = 16x
Last: (8) * (-1) = -8

Combining Like Terms

Now, we combine the like terms from the individual multiplications:

2x³ - x² + 8x² - 4x + 16x - 8

Simplifying the expression, we get:

2x³ + 7x² + 12x - 8

Conclusion

Therefore, the expanded form of (x² + 4x + 8)(2x - 1) is 2x³ + 7x² + 12x - 8. By applying the distributive property and the FOIL method, we effectively multiplied the binomials and combined the resulting terms. This process provides a clear and structured approach to expanding expressions with multiple terms.