Question

If C, equals, 3, x, squared, minus, 6C=3x
2
−6 and D, equals, 2, x, squared, plus, 1, commaD=2x
2
+1, find an expression that equals C, minus, DC−D in standard form.

Answer 1

To find the expression \( C - D \) in standard form, we need to substitute the expressions for \( C \) and \( D \) and then simplify.

Given:
\[
C = 3x^2 - 6
\]
\[
D = 2x^2 + 1
\]

Now, we compute \( C - D \):
\[
C - D = (3x^2 - 6) - (2x^2 + 1)
\]

We can distribute the negative sign:
\[
C - D = 3x^2 - 6 - 2x^2 - 1
\]

Now, we combine like terms:
1. Combine \( 3x^2 \) and \( -2x^2 \):
\[
3x^2 - 2x^2 = 1x^2 = x^2
\]

2. Combine \( -6 \) and \( -1 \):
\[
-6 - 1 = -7
\]

Putting this together, we have:
\[
C - D = x^2 - 7
\]

Thus, the expression that equals \( C - D \) in standard form is:
\[
\boxed{x^2 - 7}
\]