Question
Multiply. \[ (6 v+w)(6 v-w) \] Simplify your answer.
Ask by Murphy Dickson. in the United States
Jan 23,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The simplified answer is \(36v^2 - w^2\).
Solution
To multiply and simplify the expression \((6v + w)(6v - w)\), we can use the difference of squares formula:
\[
(a + b)(a - b) = a^2 - b^2
\]
Here, \(a = 6v\) and \(b = w\). Applying the formula:
\[
(6v + w)(6v - w) = (6v)^2 - w^2 = 36v^2 - w^2
\]
**Simplified Answer:**
\[
36v^2 - w^2
\]
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution The Deep Dive
To simplify the expression \( (6v + w)(6v - w) \), we can use the difference of squares formula, which states that \( (a + b)(a - b) = a^2 - b^2 \). Here, let \( a = 6v \) and \( b = w \). Applying the formula: \[ (6v + w)(6v - w) = (6v)^2 - w^2 \] Calculating each term: \[ (6v)^2 = 36v^2 \] \[ -w^2 = -w^2 \] Putting it all together, we get: \[ 36v^2 - w^2 \] So the simplified answer is: \[ \boxed{36v^2 - w^2} \]
