Question

Which of the following expressions is equivalent to (x–5)²?

a-x²-25
b-x²-10x+25
c-x²+10x+25
d-x²+25

Answer 1

The expression equivalent to (x-5)² is x² - 10x + 25, which corresponds to option b.

Step-by-step explanation:

The correct answer is option b: x² - 10x + 25.

To find the equivalent expression, we need to expand the square of (x-5) using the FOIL method. FOIL stands for First, Outer, Inner, Last. Applying the FOIL method, we get:

(x-5)2 = x2 - 5x - 5x + 25 = x2 - 10x + 25

Therefore, the equivalent expression is c-x²+10x+25.

To find the equivalent expression for (x-5)², we need to expand the binomial by squaring it. Squaring a binomial means multiplying the binomial by itself:

1. (x - 5)(x - 5)
2. x*x + x*(-5) + (-5)*x + (-5)*(-5)
3. x² - 5x - 5x + 25
4. x² - 10x + 25

Thus, when we square (x - 5), we get x² - 10x + 25, which matches option b.