Question
Question If \( B=1-q \) and \( C=3 q-q^{2}-1 \), find an expreasion that equals \( B-C \) in standard
Ask by Dawson Dunn. in the United States
Feb 03,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\( B - C = q^{2} - 4q + 2 \)
Solution
To find an expression for \( B - C \) in standard form, follow these steps:
Given:
\[
B = 1 - q
\]
\[
C = 3q - q^2 - 1
\]
Compute \( B - C \):
\[
B - C = (1 - q) - (3q - q^2 - 1)
\]
Distribute the negative sign:
\[
B - C = 1 - q - 3q + q^2 + 1
\]
Combine like terms:
\[
B - C = q^2 - 4q + 2
\]
So, the expression \( B - C \) in standard form is:
\[
B - C = q^2 - 4q + 2
\]
**Answer:**
After simplifying, \( B - C = q^{2} - 4\,q + 2 \).
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Simplify this solution Bonus Knowledge
To find the expression that equals \( B - C \), first we substitute the values of \( B \) and \( C \): \[ B - C = (1 - q) - (3q - q^2 - 1) \] Now, simplify the expression step by step: 1. Start by distributing the negative sign in front of \( C \): \[ B - C = (1 - q) - 3q + q^2 + 1 \] 2. Combine like terms: \[ B - C = 1 + 1 - q - 3q + q^2 \] 3. This simplifies to: \[ B - C = 2 - 4q + q^2 \] Thus, the expression that equals \( B - C \) in standard form is: \[ q^2 - 4q + 2 \]
