(x-6)-expand-and-simplify.jpeg "(x-6)(x-6) Expand And Simplify")
Expanding and Simplifying (x-6)(x-6)
This expression represents the product of two binomials: (x-6) and (x-6). To expand and simplify it, we can use the distributive property (also known as FOIL).
FOIL stands for:
- First: Multiply the first terms of each binomial.
- Outer: Multiply the outer terms of each binomial.
- Inner: Multiply the inner terms of each binomial.
- Last: Multiply the last terms of each binomial.
Let's apply FOIL to our expression:
F: x * x = x² O: x * -6 = -6x I: -6 * x = -6x L: -6 * -6 = 36
Now, we have: x² - 6x - 6x + 36
Finally, combine the like terms:
x² - 12x + 36
Therefore, the expanded and simplified form of (x-6)(x-6) is x² - 12x + 36.
Important Note: This expression is also a perfect square trinomial because it is the result of squaring a binomial (x-6). You can recognize this pattern because the first and last terms are perfect squares (x² and 36), and the middle term is twice the product of the square roots of the first and last terms (2 * x * 6 = 12x).