Question
Solve the equation \( m^{2}-16=0 \) by factoring. \[ m= \]
Ask by Wang Stewart. in the United States
Mar 09,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\( m = -4 \) or \( m = 4 \)
Solution
Solve the equation \( m^{2}-16=0 \).
Solve the quadratic equation by following steps:
- step0: Solve using square roots:
\(m^{2}-16=0\)
- step1: Add or subtract both sides:
\(m^{2}=16\)
- step2: Simplify the expression:
\(m=\pm \sqrt{16}\)
- step3: Simplify the expression:
\(m=\pm 4\)
- step4: Separate into possible cases:
\(\begin{align}&m=4\\&m=-4\end{align}\)
- step5: Rewrite:
\(m_{1}=-4,m_{2}=4\)
The solutions to the equation \(m^{2}-16=0\) by factoring are \(m=-4\) and \(m=4\).
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Simplify this solution Beyond the Answer
To solve the equation \( m^{2} - 16 = 0 \) by factoring, we can recognize that it is a difference of squares. We can rewrite it as: \[ (m - 4)(m + 4) = 0 \] Now, we can set each factor equal to zero: 1. \( m - 4 = 0 \) implies \( m = 4 \) 2. \( m + 4 = 0 \) implies \( m = -4 \) Thus, the solutions are: \[ m = 4 \text{ or } m = -4 \]
