(2x%2B6).jpeg "(2x-10)(2x+6)")
Factoring and Simplifying: (2x - 10)(2x + 6)
This expression represents the product of two binomials: (2x - 10) and (2x + 6). We can simplify this expression using the FOIL method (First, Outer, Inner, Last).
Expanding the Expression
- First: Multiply the first terms of each binomial: (2x) * (2x) = 4x²
- Outer: Multiply the outer terms of each binomial: (2x) * (6) = 12x
- Inner: Multiply the inner terms of each binomial: (-10) * (2x) = -20x
- Last: Multiply the last terms of each binomial: (-10) * (6) = -60
Now we combine these terms:
(2x - 10)(2x + 6) = 4x² + 12x - 20x - 60
Simplifying the Expression
We can simplify further by combining the like terms (the x terms):
4x² + 12x - 20x - 60 = 4x² - 8x - 60
Final Result
Therefore, the simplified form of the expression (2x - 10)(2x + 6) is 4x² - 8x - 60.
This process shows how factoring and simplifying expressions can help us understand the relationships between different mathematical expressions.