(2x%2B7).jpeg "(2x-7)(2x+7)")
Expanding the Expression (2x-7)(2x+7)
The expression (2x-7)(2x+7) is a product of two binomials. Expanding this expression involves multiplying each term in the first binomial by each term in the second binomial. We can use the FOIL method to simplify this:
FOIL stands for First, Outer, Inner, Last:
- First: Multiply the first terms of each binomial: (2x) * (2x) = 4x²
- Outer: Multiply the outer terms of each binomial: (2x) * (7) = 14x
- Inner: Multiply the inner terms of each binomial: (-7) * (2x) = -14x
- 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
This is the simplified form of the expression (2x-7)(2x+7).
Important Note: The expression (2x-7)(2x+7) is a special case known as the difference of squares. It follows the general pattern:
(a - b)(a + b) = a² - b²
In this case, 'a' is 2x and 'b' is 7. Recognizing this pattern can help you quickly expand similar expressions.