Factorize 25x2+40x+16

1. Identify the form of a perfect square trinomial, which is (ax)^2 + 2abx + b^2 = (ax + b)^2.

2. For the trinomial 25x^2 + 40x + 16, identify that 25x^2 = (5x)^2 and 16 = 4^2.

3. Check if the middle term 40x can be expressed as 2 \cdot 5x \cdot 4:

- Calculate 2 \times 5x \times 4 = 40x.

4. Since the middle term matches, we can express the trinomial as a perfect square:

25x^2 + 40x + 16 = (5x + 4)^2.

5. Concluding the factorization:

The factorized form of 25x^2 + 40x + 16 is (5x + 4)^2.