Question

If A, equals, minus, 3, plus, m, squaredA=−3+m
2
and B, equals, 3, m, plus, 4, commaB=3m+4, find an expression that equals 2, A, plus, 3, B2A+3B in standard form.

Answer 1

To find an expression that equals \( 2A + 3B \) in standard form, we first need to substitute the given expressions for \( A \) and \( B \).

Given:
\[
A = -3 + m^2
\]
\[
B = 3m + 4
\]

Now, substitute these expressions into \( 2A + 3B \):

1. Calculate \( 2A \):
\[
2A = 2(-3 + m^2) = 2(-3) + 2(m^2) = -6 + 2m^2
\]

2. Calculate \( 3B \):
\[
3B = 3(3m + 4) = 3 \cdot 3m + 3 \cdot 4 = 9m + 12
\]

3. Now add \( 2A \) and \( 3B \):
\[
2A + 3B = (-6 + 2m^2) + (9m + 12)
\]

Combine the terms:
\[
= 2m^2 + 9m + (-6 + 12)
\]
\[
= 2m^2 + 9m + 6
\]

The expression \( 2A + 3B \) in standard form is:
\[
\boxed{2m^2 + 9m + 6}
\]