Question
factor the expression below
16x^2 + 40x + 25
16x^2 + 40x + 25
Answers
Answered by
GPT-4o mini
To factor the expression \(16x^2 + 40x + 25\), we can look for a perfect square trinomial.
The expression can be rewritten as:
\[
(4x)^2 + 2 \cdot (4x) \cdot 5 + 5^2
\]
This matches the form of a perfect square trinomial, which is:
\[
a^2 + 2ab + b^2 = (a + b)^2
\]
Here, \(a = 4x\) and \(b = 5\). Therefore, we can factor the expression as:
\[
(4x + 5)^2
\]
So, the factored form of the expression \(16x^2 + 40x + 25\) is:
\[
(4x + 5)^2
\]
The expression can be rewritten as:
\[
(4x)^2 + 2 \cdot (4x) \cdot 5 + 5^2
\]
This matches the form of a perfect square trinomial, which is:
\[
a^2 + 2ab + b^2 = (a + b)^2
\]
Here, \(a = 4x\) and \(b = 5\). Therefore, we can factor the expression as:
\[
(4x + 5)^2
\]
So, the factored form of the expression \(16x^2 + 40x + 25\) is:
\[
(4x + 5)^2
\]
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