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

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 \( b = 9 \).

1. Identify the expression as a difference of squares.
2. Apply the difference of squares formula.

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

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

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

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

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

Final Answer