how do you factor 4x²+20x+25?

4x^2 + 20x + 25
= 4x^2 + 10x + 10x + 25
= (4x^2 + 10x) + (10x + 25)
= 2x(2x + 5) + 5(2x + 5)
= (2x + 5)(2x + 5)
= (2x + 5)^2

1st factor:
4x² + 20x + 25 = 0
4x² + 20x = - 25
x² + 5x = - 25/4
x² + 5/2x = - 25/4 + (5/2)²
x² + 5/2 = - 25/4 + 25/4
(x + 5/2)² = 0
= x + 5/2
= 2x + 5

2nd factor:
= (4x² + 20x + 25)/(2x + 5)
= 2x + 5

Answer: (2x + 5)(2x + 5) or simply (2x + 5)²

(2x + 5)(2x + 5)

4x^2 + 20x + 25
= (2x)^2 + 2x * 5 * 2 +5^2
= (2x + 5) ^2

(2x+5)^2