Question
What is the coefficient of the second term of the trinomial?
(3x+3)2=9x2+Bx+9
(3x+3)2=9x2+Bx+9
Answers
Answered by
GPT-4o mini
To find the coefficient of the second term of the trinomial from the equation
\[
(3x + 3)^2 = 9x^2 + Bx + 9,
\]
we first need to expand the left side of the equation:
\[
(3x + 3)^2 = (3x)^2 + 2(3x)(3) + (3)^2.
\]
Calculating each term:
1. \((3x)^2 = 9x^2\),
2. \(2(3x)(3) = 18x\),
3. \((3)^2 = 9\).
Now we combine these results:
\[
(3x + 3)^2 = 9x^2 + 18x + 9.
\]
From this expansion, we can now compare it to the given trinomial:
\[
9x^2 + Bx + 9.
\]
It is clear that \(B\) corresponds to the coefficient of the \(x\) term. Therefore, we identify:
\[
B = 18.
\]
Thus, the coefficient of the second term of the trinomial is
\[
\boxed{18}.
\]
\[
(3x + 3)^2 = 9x^2 + Bx + 9,
\]
we first need to expand the left side of the equation:
\[
(3x + 3)^2 = (3x)^2 + 2(3x)(3) + (3)^2.
\]
Calculating each term:
1. \((3x)^2 = 9x^2\),
2. \(2(3x)(3) = 18x\),
3. \((3)^2 = 9\).
Now we combine these results:
\[
(3x + 3)^2 = 9x^2 + 18x + 9.
\]
From this expansion, we can now compare it to the given trinomial:
\[
9x^2 + Bx + 9.
\]
It is clear that \(B\) corresponds to the coefficient of the \(x\) term. Therefore, we identify:
\[
B = 18.
\]
Thus, the coefficient of the second term of the trinomial is
\[
\boxed{18}.
\]