Questions: Multiply using the rule for the product of the sum and difference of two terms. (6x+7)(6x-7)

Solution Steps

The expression \((6x + 7)(6x - 7)\) can be simplified using the difference of squares formula, which states that \((a + b)(a - b) = a^2 - b^2\). Here, \(a = 6x\) and \(b = 7\).

We start with the expression \((6x + 7)(6x - 7)\). This expression can be simplified using the difference of squares formula.

Using the formula \((a + b)(a - b) = a^2 - b^2\), we identify \(a = 6x\) and \(b = 7\). Thus, we can rewrite the expression as: \[ (6x + 7)(6x - 7) = (6x)^2 - (7)^2 \]

Now, we calculate the squares: \[ (6x)^2 = 36x^2 \quad \text{and} \quad (7)^2 = 49 \] Substituting these values back into the expression gives us: \[ 36x^2 - 49 \]

Final Answer