Question

Factor the expression below.
25x^2+ 20x+4
0(5x - 2)(5x-2)
0(25x -2)(x-2)
0(5x + 2)(5x + 2)
0(25x + +2)(x+2)

Answer 1

To factor the expression \( 25x^2 + 20x + 4 \), we can first look for a perfect square trinomial, since the coefficients are perfect squares.

1. The first term \( 25x^2 \) is \( (5x)^2 \).
2. The last term \( 4 \) is \( (2)^2 \).
3. The middle term \( 20x \) can be rewritten as \( 2 \cdot 5x \cdot 2 \).

Thus, we can express the trinomial as:

\[
(5x + 2)(5x + 2) \quad \text{or} \quad (5x + 2)^2
\]

Therefore, the factored form of \( 25x^2 + 20x + 4 \) is:

\[
(5x + 2)^2
\]

So, the only correct option is:

\[
0(5x + 2)(5x + 2)
\]

However, it looks like the options you provided were not perfectly aligned with the correct factorization. It seems like a mistake in the format since `0` should not be part of the factorization.

But the accurate factorization of \( 25x^2 + 20x + 4 \) is:

\[
(5x + 2)^2
\]