%5E2-find-the-product.jpeg "(a-6)^2 Find The Product")
Finding the Product of (a - 6)^2
The expression (a - 6)^2 represents the square of the binomial (a - 6). To find the product, we can use the FOIL method or the square of a binomial formula.
Using the FOIL Method
FOIL stands for First, Outer, Inner, Last. It's a helpful acronym for remembering how to multiply two binomials.
- First: Multiply the first terms of each binomial: a * a = a^2
- Outer: Multiply the outer terms of the binomials: a * -6 = -6a
- Inner: Multiply the inner terms of the binomials: -6 * a = -6a
- Last: Multiply the last terms of each binomial: -6 * -6 = 36
Now, add all the terms together: a^2 - 6a - 6a + 36
Combine like terms: a^2 - 12a + 36
Using the Square of a Binomial Formula
The square of a binomial formula states: (x - y)^2 = x^2 - 2xy + y^2
Applying this to our expression: (a - 6)^2 = a^2 - 2(a)(6) + 6^2
Simplifying: a^2 - 12a + 36
Conclusion
Both methods arrive at the same answer: (a - 6)^2 = a^2 - 12a + 36. You can choose the method you find easiest to understand and apply.