%5E2-simplify.jpeg "(x-4)^2 Simplify")
Simplifying (x - 4)^2
The expression (x - 4)^2 represents the square of the binomial (x - 4). To simplify it, we can use the FOIL method or the square of a binomial formula.
Using FOIL Method
FOIL stands for First, Outer, Inner, Last. This method helps us multiply two binomials.
- First: Multiply the first terms of each binomial: x * x = x^2
- Outer: Multiply the outer terms of the binomials: x * -4 = -4x
- Inner: Multiply the inner terms of the binomials: -4 * x = -4x
- Last: Multiply the last terms of each binomial: -4 * -4 = 16
Now, combine the like terms:
x^2 - 4x - 4x + 16
Therefore, (x - 4)^2 simplifies to x^2 - 8x + 16.
Using Square of a Binomial Formula
The square of a binomial formula states:
(a - b)^2 = a^2 - 2ab + b^2
Applying this to our expression:
a = x b = 4
(x - 4)^2 = x^2 - 2(x)(4) + 4^2
Simplifying the expression:
(x - 4)^2 = x^2 - 8x + 16
Both methods arrive at the same answer: x^2 - 8x + 16.
Remember, simplifying an expression means rewriting it in a more concise form without changing its value. By using either the FOIL method or the square of a binomial formula, we have successfully simplified (x - 4)^2.