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