Questions: Write the expression in factored form. 49 m^2 - n^2

Write the expression in factored form. 49 m^2 - n^2
Transcript text: Write the expression in factored form. \[ 49 m^{2}-n^{2} \]
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Solution

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Solution Steps

Step 1: Identify the structure of the expression

The given expression is \( 49m^{2} - n^{2} \). This is a difference of squares, which follows the form \( a^{2} - b^{2} \).

Step 2: Rewrite the expression as a difference of squares

Express \( 49m^{2} \) as \( (7m)^{2} \) and \( n^{2} \) as \( (n)^{2} \). The expression becomes: \[ (7m)^{2} - (n)^{2} \]

Step 3: Apply the difference of squares formula

The difference of squares formula is \( a^{2} - b^{2} = (a + b)(a - b) \). Applying this to the expression: \[ (7m + n)(7m - n) \]

Final Answer

\(\boxed{(7m + n)(7m - n)}\)

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