Question

question
if a = r - 2 and b = r² - 4r + 5, find an expression that equals 3a + 2b in standard form.
answer
attempt 1 out of 2
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Explanation:

Step1: Substitute A and B into the expression

We know that \( A = r - 2 \) and \( B = r^{2}-4r + 5 \). So we substitute these into \( 3A + 2B \):
\( 3(r - 2)+2(r^{2}-4r + 5) \)

Step2: Distribute the coefficients

First, distribute the 3 in \( 3(r - 2) \): \( 3\times r-3\times2=3r - 6 \)
Then, distribute the 2 in \( 2(r^{2}-4r + 5) \): \( 2\times r^{2}-2\times4r+2\times5 = 2r^{2}-8r + 10 \)

Step3: Combine like terms

Now we have \( 3r - 6+2r^{2}-8r + 10 \). Combine the \( r \) terms: \( 3r-8r=-5r \)
Combine the constant terms: \( -6 + 10 = 4 \)
So the expression becomes \( 2r^{2}-5r + 4 \)

Answer:

\( 2r^{2}-5r + 4 \)