Question

arithmetic on polynomial expressions
score: 1/5 penalty: 0.25 off
question
if b = -t - 1 and c = 3t - 2, find an expression that equals b - 2c in standard form.
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answer attempt 1 out of 2

Explanation:

Step1: Substitute B and C into B - 2C

Given \( B = -t - 1 \) and \( C = 3t - 2 \), we substitute these into the expression \( B - 2C \). So we have \( (-t - 1) - 2(3t - 2) \).

Step2: Distribute the -2

Using the distributive property \( a(b + c)=ab+ac \), we distribute the -2 to \( 3t \) and -2. So \( -2(3t - 2)=-6t + 4 \). Now the expression becomes \( -t - 1 - 6t + 4 \).

Step3: Combine like terms

Combine the \( t \)-terms: \( -t-6t=-7t \). Combine the constant terms: \( -1 + 4 = 3 \). So the simplified expression is \( -7t + 3 \).

Answer:

\( -7t + 3 \)