Problem 17 - Introductory Algebra for College Students

Question

Multiply as indicated. $$\left(y^{2}-9\right) \cdot \frac{4}{y-3}$$

Step-by-Step Solution

Answer

The result of the multiplication is \(4y + 12\).

Step 1: Identify Difference of Squares

The binomial \(y^2 - 9\) is a difference of squares, because it can be written as \(y^2 - 3^2\).

Step 2: Factor the Difference of Squares

Difference of squares can be factored into \((a+b)(a-b)\), so \(y^2 - 9\) becomes \((y-3)(y+3)\). Thus the expression becomes \((y-3)(y+3) \cdot \frac{4}{y-3}\).

Step 3: Simplify the Expression

Notice that \((y-3)\) in the binomial and the denominator of the fraction can cancel each other out, the expression simplifies to \((y+3) \cdot 4 = 4y +12\)