Question

find the product. simplify your answer.
(2u + 2)(4u - 4)

Explanation:

Step1: Apply the distributive property (FOIL method)

Multiply the First terms: \(2u \times 4u = 8u^2\)
Multiply the Outer terms: \(2u \times (-4) = -8u\)
Multiply the Inner terms: \(2 \times 4u = 8u\)
Multiply the Last terms: \(2 \times (-4) = -8\)
So we have \(8u^2 - 8u + 8u - 8\)

Step2: Combine like terms

The \(-8u\) and \(8u\) cancel out, leaving \(8u^2 - 8\)
We can also factor out a common factor of 8: \(8(u^2 - 1)\)
And further factor using the difference of squares: \(8(u - 1)(u + 1)\) (but the simplified polynomial form is \(8u^2 - 8\))

Answer:

\(8u^2 - 8\)