Question
Multiply. \begin{tabular}{ll}\( (6-5 c)(6+5 c) \) \\ Simplify your answer. \\ \hline\( \square \) & \( \times \) \\ \hline\end{tabular}
Ask by Hodgson Li. in the United States
Jan 29,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\[
36 - 25c^2
\]
Solution
To multiply and simplify the expression \((6 - 5c)(6 + 5c)\), you can use the **difference of squares** formula:
\[
(a - b)(a + b) = a^2 - b^2
\]
Here, \(a = 6\) and \(b = 5c\). Applying the formula:
\[
(6 - 5c)(6 + 5c) = 6^2 - (5c)^2 = 36 - 25c^2
\]
**Simplified Answer:**
\[
36 - 25c^2
\]
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Extra Insights
To multiply \( (6-5c)(6+5c) \), we can use the difference of squares formula, which states that \( (a-b)(a+b) = a^2 - b^2 \). Here, let \( a = 6 \) and \( b = 5c \). Applying the formula: \[ (6-5c)(6+5c) = 6^2 - (5c)^2 \] Calculating each part: \[ 6^2 = 36 \quad \text{and} \quad (5c)^2 = 25c^2 \] Now, substituting back into the equation: \[ 36 - 25c^2 \] So, the simplified answer is: \[ \boxed{36 - 25c^2} \]
