Question

Find the product. $$ (x-2)(x-7) $$

Short answer

The product of the binomials \(x - 2\) and \(x - 7\) is \(x^2 - 9x + 14\).

Step-by-step solution

Identify the Terms

Two binomials to multiply are: \(x - 2\) and \(x - 7\). These binomials have two terms each: \(x\) and \(-2\) in the first, and \(x\) and \(-7\) in the second.

Apply FOIL Method - First terms

First, multiply the First elements in each binomial which are \(x\) from \(x - 2\) and \(x\) from \(x - 7\). This results in \(x^2\).

Apply FOIL Method - Outer terms

Then, Multiply the Outer elements in the binomials, which are \(x\) from \(x - 2\) and \(-7\) from \(x - 7\). This results in \(-7x\).

Apply FOIL Method - Inner terms

Next, multiply the Inner elements in the binomials, which are \(-2\) from \(x - 2\) and \(x\) from \(x - 7\). This results in \(-2x\).

Apply FOIL Method - Last terms

Finally, multiply the Last elements in the binomials, which are \(-2\) from \(x - 2\) and \(-7\) from \(x - 7\). This results in \(14\).

Combine like terms

Combine all found products, which are \(x^2\), \(-7x\), \(-2x\), and \(14\). This results in \(x^2 - 7x - 2x + 14\). Combine \(-7x\) and \(-2x\) to get \(-9x\). Thus, the product of the two binomials is \(x^2 - 9x + 14\).