Question

Find the product. $$ (x+6)(x-7) $$

Short answer

The product of the given binomial expression \( (x+6)(x-7) \) is \( x^2 - x - 42 \).

Step-by-step solution

Identify the Binomials

Identify the binomials in the expression. Here, \(x+6\) and \(x-7\) are the binomials that need to be multiplied.

Apply the Distributive Property - First Round

Firstly, multiply the first term of the first binomial \(x\) with both the terms of the second binomial \((x-7)\). This gives \(x \cdot x - x \cdot 7\) which simplifies to \(x^2 - 7x\).

Apply the Distributive Property - Second Round

Next, multiply the second term of the first binomial \(6\) with both the terms of the second binomial \((x-7)\). This gives \(6 \cdot x - 6 \cdot 7\) which simplifies to \(6x - 42\).

Combine Like Terms

Now, combine the expressions obtained in Step 2 and Step 3: \(x^2 - 7x + 6x - 42\). The terms \(-7x\) and \(6x\) are similar and can be combined to \(-x\). So, the final simplified expression becomes: \(x^2 - x - 42\).