Questions: Multiply as indicated. [ (y^2-64) cdot frac6y-8 ] ((y^2-64) cdot frac6y-8=) (square) (Simplify your answer.)

$Multiply as indicated. [ (y^2-64) cdot frac6y-8 ] ((y^2-64) cdot frac6y-8=) (square) (Simplify your answer.)$

Transcript text: Multiply as indicated. \[ \left(y^{2}-64\right) \cdot \frac{6}{y-8} \] $\left(y^{2}-64\right) \cdot \frac{6}{y-8}=$ $\square$ (Simplify your answer.)

Solution

Solution Steps

Step 1: Factor the Polynomial

We start with the expression $ y^2 - 64 $. This can be factored using the difference of squares formula: \[ y^2 - 64 = (y - 8)(y + 8) \]

Step 2: Set Up the Multiplication

Next, we multiply the factored form of the polynomial by the rational expression $ \frac{6}{y - 8} $: \[ (y - 8)(y + 8) \cdot \frac{6}{y - 8} \]

Step 3: Simplify the Expression

In this multiplication, the $ (y - 8) $ in the numerator and denominator cancels out: \[ \frac{(y - 8)(y + 8) \cdot 6}{y - 8} = 6(y + 8) \]

Step 4: Final Simplification

Distributing the $ 6 $ gives us the final simplified expression: \[ 6(y + 8) = 6y + 48 \]

Final Answer

$\boxed{6y + 48}$

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