Problem 43 - Algebra 1: Concepts and Skills

Question

Find the product. $$ (3 x-4 y)(3 x+4 y) $$

Step-by-Step Solution

Answer

\(9x^2 - 16y^2\)

Step 1: Apply the FOIL Method: First Terms

Multiply the first terms of each binomial. In this case, the first terms are \(3x\) and \(3x\), which gives \(3x \cdot 3x = 9x^2\).

Step 2: Apply the FOIL Method: Outer Terms

Multiply the outer terms of each binomial. In this case, the outer terms are \(3x\) and \(4y\), which gives \(3x \cdot 4y = 12xy\).

Step 3: Apply the FOIL Method: Inner Terms

Multiply the inner terms of each binomial. In this case, the inner terms are \(-4y\) and \(3x\), which gives \(-4y \cdot 3x = -12xy\).

Step 4: Apply the FOIL Method: Last Terms

Multiply the last terms of each binomial. In this case, the last terms are \(-4y\) and \(4y\), which gives \(-4y \cdot 4y = -16y^2\).

Step 5: Combine Like Terms

Add the products from steps 1-4. The \(12xy\) and \(-12xy\) cancel each other out, resulting in the equation \(9x^2 - 16y^2\).