(2x+7)(2x-7) Answer

Jasonbradley

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Jun 16, 2024

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Expanding the Expression (2x + 7)(2x - 7)

This expression represents the product of two binomials. To find the answer, we can use the FOIL method which stands for First, Outer, Inner, Last.

Here's how it works:

1. First: Multiply the first terms of each binomial: (2x) * (2x) = 4x²
2. Outer: Multiply the outer terms of the binomials: (2x) * (-7) = -14x
3. Inner: Multiply the inner terms of the binomials: (7) * (2x) = 14x
4. Last: Multiply the last terms of each binomial: (7) * (-7) = -49

Now, combine all the terms:

4x² - 14x + 14x - 49

Notice that the middle terms (-14x and +14x) cancel each other out. This leaves us with:

4x² - 49

Therefore, the answer to (2x + 7)(2x - 7) is 4x² - 49.

Important Note: This type of expression, where you have the sum and difference of the same two terms, is known as the difference of squares. The general form of the difference of squares is: (a + b)(a - b) = a² - b²

Recognizing this pattern can make simplifying such expressions much faster.