To factor the quadratic expression x² + 8x + 16, we first look for two numbers that multiply to give us 16 (the constant term) and add to give us 8 (the coefficient of the linear term).
The numbers that satisfy these conditions are 4 and 4, since:
- 4 * 4 = 16
- 4 + 4 = 8
Thus, we can express the original quadratic as:
(x + 4)(x + 4) or (x + 4)².
So, the factored form of the expression x² + 8x + 16 is (x + 4)².