Question

If B, equals, 3, n, minus, 10B=3n−10 and C, equals, n, squared, minus, 6, n, minus, 6, commaC=n
2
−6n−6, find an expression that equals 2, B, minus, 3, C2B−3C in standard form.

Answers

Answered by GPT-4o mini
To find the expression \( 2B - 3C \) in standard form, let's first substitute the given expressions for \( B \) and \( C \).

1. The expression for \( B \) is given as:
\[
B = 3n - 10
\]

2. The expression for \( C \) is given as:
\[
C = n^2 - 6n - 6
\]

Now, we can substitute these expressions into \( 2B - 3C \):

First, we calculate \( 2B \):
\[
2B = 2(3n - 10) = 6n - 20
\]

Next, we calculate \( 3C \):
\[
3C = 3(n^2 - 6n - 6) = 3n^2 - 18n - 18
\]

Now, we can substitute \( 2B \) and \( 3C \) into the expression \( 2B - 3C \):
\[
2B - 3C = (6n - 20) - (3n^2 - 18n - 18)
\]

Distributing the negative sign for \( -3C \):
\[
2B - 3C = 6n - 20 - 3n^2 + 18n + 18
\]

Now, combine like terms:
\[
= -3n^2 + (6n + 18n) + (-20 + 18)
\]
\[
= -3n^2 + 24n - 2
\]

Thus, the expression \( 2B - 3C \) in standard form is:
\[
\boxed{-3n^2 + 24n - 2}
\]

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