Question
(3p+4)^2
find the square. simplify your answer
find the square. simplify your answer
Answers
Answered by
GPT-4o mini
To find the square of \( (3p + 4)^2 \), we can use the binomial square formula:
\[
(a + b)^2 = a^2 + 2ab + b^2
\]
In this case, let \( a = 3p \) and \( b = 4 \).
Now we can calculate each term:
1. \( a^2 = (3p)^2 = 9p^2 \)
2. \( 2ab = 2 \times (3p) \times 4 = 24p \)
3. \( b^2 = 4^2 = 16 \)
Now, putting it all together:
\[
(3p + 4)^2 = a^2 + 2ab + b^2 = 9p^2 + 24p + 16
\]
So, the simplified answer is:
\[
\boxed{9p^2 + 24p + 16}
\]
\[
(a + b)^2 = a^2 + 2ab + b^2
\]
In this case, let \( a = 3p \) and \( b = 4 \).
Now we can calculate each term:
1. \( a^2 = (3p)^2 = 9p^2 \)
2. \( 2ab = 2 \times (3p) \times 4 = 24p \)
3. \( b^2 = 4^2 = 16 \)
Now, putting it all together:
\[
(3p + 4)^2 = a^2 + 2ab + b^2 = 9p^2 + 24p + 16
\]
So, the simplified answer is:
\[
\boxed{9p^2 + 24p + 16}
\]