%5E2.jpeg "(-5x+7)^2")
Expanding the Square of a Binomial: (-5x + 7)^2
The expression (-5x + 7)^2 represents the square of a binomial. To expand this expression, we can apply the FOIL method or the square of a binomial pattern.
Using the FOIL Method
FOIL stands for First, Outer, Inner, Last. This method helps us to multiply two binomials systematically.
- First: Multiply the first terms of each binomial: (-5x) * (-5x) = 25x²
- Outer: Multiply the outer terms: (-5x) * 7 = -35x
- Inner: Multiply the inner terms: 7 * (-5x) = -35x
- Last: Multiply the last terms: 7 * 7 = 49
Now, we add all the products together: 25x² - 35x - 35x + 49
Combining like terms, we get the final expanded form: 25x² - 70x + 49
Using the Square of a Binomial Pattern
The square of a binomial pattern is: (a + b)² = a² + 2ab + b²
In our case, a = -5x and b = 7. Substituting these values into the pattern:
(-5x)² + 2(-5x)(7) + 7²
Simplifying: 25x² - 70x + 49
Both methods result in the same expanded form: 25x² - 70x + 49
Therefore, the expanded form of (-5x + 7)² is 25x² - 70x + 49.