Math Tutorial: How to Factor the Expression x^2 – 8x + 16

x^2 – 8x + 16

To begin, let’s factor the expression x^2 – 8x + 16

To begin, let’s factor the expression x^2 – 8x + 16.

1. Look at the constant term (16) and consider its factors. The factors of 16 are 1 and 16, 2 and 8, and 4 and 4.

2. Now, we need to find the pair of factors that adds up to the coefficient of x (-8). From the possible factor pairs, we see that 4 and 4 add up to 8. Therefore, the desired pair of factors is (4, 4).

3. Rewrite the middle term (-8x) by splitting it into two terms using the pair of factors found in step 2, as follows: -4x-4x.

Now, we can rewrite the expression:

x^2 – 4x – 4x + 16

4. We can now group the terms together:

(x^2 – 4x) + (-4x + 16)

5. Now, factor out the common factors separately from each group:

x(x – 4) – 4(x – 4)

6. Notice that both groups have a common factor, (x – 4). Factor it out:

(x – 4)(x – 4)

So, the fully factored expression is (x – 4)(x – 4) or (x – 4)^2.

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