If B, equals, 3, n, minus, 10B=3n−10 and C, equals, n, squared, minus, 6, n, minus, 6, commaC=n

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.

GPT-4o mini · Answer

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: $$ \boxed{-3n^2 + 24n - 2} $$