(6x-7)^2

Jasonbradley

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Jun 16, 2024

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Expanding the Square of a Binomial: (6x - 7)²

In mathematics, the square of a binomial is a common expression that can be simplified using the FOIL method. This article will guide you through the process of expanding the expression (6x - 7)².

Understanding the FOIL Method

The FOIL method 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 the binomials.
• Inner: Multiply the inner terms of the binomials.
• Last: Multiply the last terms of each binomial.

Expanding (6x - 7)²

Let's apply the FOIL method to expand the given expression:

1. Rewrite the expression: (6x - 7)² = (6x - 7)(6x - 7)

2. First: (6x)(6x) = 36x²

3. Outer: (6x)(-7) = -42x

4. Inner: (-7)(6x) = -42x

5. Last: (-7)(-7) = 49

6. Combine the terms: 36x² - 42x - 42x + 49

7. Simplify: 36x² - 84x + 49

Final Result

Therefore, the expanded form of (6x - 7)² is 36x² - 84x + 49.