Question
(4x^2+10x)+(10x+25) factored
Answers
Answered by
GPT-4o mini
To factor the expression \( (4x^2 + 10x) + (10x + 25) \), you can first combine like terms:
\[
4x^2 + 10x + 10x + 25 = 4x^2 + 20x + 25
\]
Now, we can factor \( 4x^2 + 20x + 25 \). Notice that this is a quadratic expression. We can look for two numbers that multiply to \( 4 \cdot 25 = 100 \) and add up to \( 20 \).
The numbers that satisfy this are \( 10 \) and \( 10 \).
Next, we can rewrite the quadratic expression:
\[
4x^2 + 10x + 10x + 25 = 4x^2 + 10x + 10x + 25
\]
Now, group the terms:
\[
(4x^2 + 10x) + (10x + 25)
\]
We can factor by grouping:
\[
2x(2x + 5) + 5(2x + 5)
\]
Now factor out the common factor, which is \( (2x + 5) \):
\[
(2x + 5)(2x + 5) \quad \text{or} \quad (2x + 5)^2
\]
Thus, the factored form of the expression is:
\[
(2x + 5)^2
\]
\[
4x^2 + 10x + 10x + 25 = 4x^2 + 20x + 25
\]
Now, we can factor \( 4x^2 + 20x + 25 \). Notice that this is a quadratic expression. We can look for two numbers that multiply to \( 4 \cdot 25 = 100 \) and add up to \( 20 \).
The numbers that satisfy this are \( 10 \) and \( 10 \).
Next, we can rewrite the quadratic expression:
\[
4x^2 + 10x + 10x + 25 = 4x^2 + 10x + 10x + 25
\]
Now, group the terms:
\[
(4x^2 + 10x) + (10x + 25)
\]
We can factor by grouping:
\[
2x(2x + 5) + 5(2x + 5)
\]
Now factor out the common factor, which is \( (2x + 5) \):
\[
(2x + 5)(2x + 5) \quad \text{or} \quad (2x + 5)^2
\]
Thus, the factored form of the expression is:
\[
(2x + 5)^2
\]