Question

Does 4x^2-20x+25 equal (2x-5)^2?

Answer 1

Answer:

Step-by-step explanation:

(2x-5)² = (2x)² - (2x⋅5) - (2x⋅5) + (-5)²

= 4x² - 20x + 25

Answer 2

Answer:

4x^2-20x+25 DOES equal (2x-5)^2.

Step-by-step explanation:

By factoring 4x^2-20x+25, we have:

4x^2-20x+25 = (2x - 5)(2x - 5) because of the order for this multiplication as FOIL, or first, outside, inside, and last.

Firstly, we take the first numbers 2x * 2x = 4x, so we put this down as

4x^2

We then take the outside numbers 2x * -5 = -10x and also put this down

4x^2 - 10x

We then take the inside numbers 2x * -5 = -10x again and put this down

4x^2 - 10x - 10x, or 4x^2 - 20x

We then take the last numbers -5 * -5 = +25 and put this down

4x^2 - 20 + 25

We now know that 4x^2 - 20 + 25 is equal to (2x - 5)(2x - 5), and

(2x - 5)(2x - 5) is equal to (2x - 5)^2.