(6n2-6n-5)(7n2+6n-5)

2 min read Jun 16, 2024

Multiplying Binomials: (6n²-6n-5)(7n²+6n-5)

This article will guide you through the process of multiplying the two binomials: (6n²-6n-5)(7n²+6n-5). We will use the FOIL method to simplify the expression.

Understanding the FOIL Method

FOIL is an acronym that stands for First, Outer, Inner, Last. It's a mnemonic device used to remember the steps for multiplying two binomials.

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

Applying the FOIL Method to Our Problem

Let's break down the multiplication of (6n²-6n-5)(7n²+6n-5) using the FOIL method:

First: (6n²) * (7n²) = 42n⁴
Outer: (6n²) * (6n) = 36n³
Inner: (-6n) * (7n²) = -42n³
Last: (-6n) * (6n) = -36n²
First: (6n²) * (-5) = -30n²
Outer: (-6n) * (-5) = 30n
Inner: (-5) * (7n²) = -35n²
Last: (-5) * (6n) = -30n
Last: (-5) * (-5) = 25

Combining Like Terms

Now, we have the following terms:

42n⁴ + 36n³ - 42n³ - 36n² - 30n² + 30n - 35n² - 30n + 25

Combining like terms:

42n⁴ + (36n³ - 42n³) + (-36n² - 30n² - 35n²) + (30n - 30n) + 25

This simplifies to:

42n⁴ - 6n³ - 101n² + 25

Conclusion

By using the FOIL method, we successfully multiplied the binomials (6n²-6n-5)(7n²+6n-5) and obtained the simplified expression 42n⁴ - 6n³ - 101n² + 25.