Questions: c^2-81 c^2-81=square

c^2-81 c^2-81=square
Transcript text: c^{2}-81 \\ c^{2}-81=\square
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Solution

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Solution Steps

To solve the given expression \( c^2 - 81 \), we can recognize it as a difference of squares. The difference of squares formula is \( a^2 - b^2 = (a - b)(a + b) \). Here, \( a = c \) and \( b = 9 \).

Solution Approach
  1. Identify the expression as a difference of squares.
  2. Apply the difference of squares formula.
Step 1: Recognize the Expression as a Difference of Squares

The given expression is \( c^2 - 81 \). This can be identified as a difference of squares, which follows the formula: \[ a^2 - b^2 = (a - b)(a + b) \]

Step 2: Apply the Difference of Squares Formula

In this case, \( a = c \) and \( b = 9 \). Therefore, we can rewrite the expression as: \[ c^2 - 81 = (c - 9)(c + 9) \]

Step 3: Substitute the Given Value of \( c \)

Given \( c = 5 \), we substitute this value into the factored form: \[ (5 - 9)(5 + 9) \]

Step 4: Simplify the Expression

Simplify the terms inside the parentheses: \[ (5 - 9) = -4 \] \[ (5 + 9) = 14 \]

Step 5: Calculate the Product

Multiply the simplified terms: \[ (-4) \times 14 = -56 \]

Final Answer

\(\boxed{c^2 - 81 = (c - 9)(c + 9)}\)

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