Factor completely x2 − 8x + 16.
(x + 4)(x + 4)
(x − 4)(x − 4)
(x + 4)(x − 4)
(x − 2)(x − 8)
i don't understand this
No. (x+4)(x-4) = x^2-16
(x-4)(x-4) = x^2-8x+16
so the second one?
To factor the expression x^2 - 8x + 16 completely, you can use a method called "factoring by grouping". Here's a step-by-step explanation of how to do it:
Step 1: Look for any common factors among the terms. In this case, there are no common factors.
Step 2: Split the middle term (-8x) into two terms whose coefficients multiply to give you the constant term (16) and whose coefficients add up to give you the coefficient of the middle term (-8). The numbers that satisfy these conditions are -4 and -4. So, we rewrite -8x as -4x - 4x.
Step 3: Factor by grouping. Rearrange the expression by grouping the terms into two pairs. In this case, we have x^2 - 4x - 4x + 16.
Step 4: Factor out the greatest common factor from each pair. In the first pair, x^2 - 4x, the greatest common factor is x. Factoring it out, we get x(x - 4). In the second pair, -4x + 16, the greatest common factor is -4. Factoring it out, we get -4(x - 4).
Step 5: Combine the factored pairs to get the final answer. The factored pairs are x(x - 4) - 4(x - 4). Since both pairs have the common factor (x - 4), we can factor it out. This gives us (x - 4)(x - 4), which can be simplified as (x - 4)^2.
Therefore, the correct answer to factor the expression x^2 - 8x + 16 completely is (x - 4)^2. So, the correct option is "(x - 4)(x - 4)".
(x + 4)(x − 4)
Find the GCF and then factor it in the solution