Question

If A, equals, 2, r, squared, plus, 6, r, plus, 1A=2r
2
+6r+1 and B, equals, 2, r, minus, 6, commaB=2r−6, find an expression that equals 2, A, minus, 3, B2A−3B in standard form.

Answer 1

To find the expression \(2A - 3B\) in standard form, we start by substituting the expressions for \(A\) and \(B\):

Given:
\[
A = 2r^2 + 6r + 1
\]
\[
B = 2r - 6
\]

Now we will calculate \(2A\) and \(3B\).

1. **Calculate \(2A\)**:
\[
2A = 2(2r^2 + 6r + 1) = 4r^2 + 12r + 2
\]

2. **Calculate \(3B\)**:
\[
3B = 3(2r - 6) = 6r - 18
\]

3. **Now substitute \(2A\) and \(3B\) into \(2A - 3B\)**:
\[
2A - 3B = (4r^2 + 12r + 2) - (6r - 18)
\]

4. **Distributing the negative sign**:
\[
2A - 3B = 4r^2 + 12r + 2 - 6r + 18
\]

5. **Combine like terms**:
\[
2A - 3B = 4r^2 + (12r - 6r) + (2 + 18)
\]
\[
= 4r^2 + 6r + 20
\]

Thus, the expression \(2A - 3B\) in standard form is:
\[
\boxed{4r^2 + 6r + 20}
\]