x^2 + 8x + 16
(x + 4)^2
The expression x^2 + 8x + 16 can be factored as (x+4)(x+4), or simply (x+4)^2.
To see why, you can use the factoring technique known as completing the square. Here’s how it works:
Take half of the coefficient of x (which is 8 in this case): 8/2 = 4
Square the result from step 1: 4^2 = 16
Add and subtract the result from step 2 inside the parentheses: x^2 + 8x + 16 – 16 = (x+4)^2 – 16
Simplify the expression from step 3: x^2 + 8x + 16 – 16 = (x+4)^2 – 16
So we have the expression x^2 + 8x + 16 = (x+4)^2.
This is an example of factoring a perfect square trinomial, which can be useful for solving equations and graphing quadratic functions.
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