Question

select the expressions that are equivalent to -8(-2w - 2).
16w + 16
(-6w + 4w - 2)·-8
-8(-8w + 6w - 2)
(-2w - 2)·-8

Explanation:

Step1: Simplify the original expression

We use the distributive property \(a(b + c)=ab+ac\). For \(-8(-2w - 2)\), we have \((-8)\times(-2w)+(-8)\times(-2)=16w + 16\).

Step2: Analyze \(16w + 16\)

This is the simplified form of the original expression, so it is equivalent.

Step3: Analyze \((-6w + 4w - 2)\cdot(-8)\)

First, simplify inside the parentheses: \(-6w+4w - 2=-2w - 2\). Then multiply by \(-8\): \((-2w - 2)\times(-8)=16w + 16\), which is equivalent.

Step4: Analyze \(-8(-8w + 6w - 2)\)

Simplify inside the parentheses: \(-8w+6w - 2=-2w - 2\). Then multiply by \(-8\): \(-8\times(-2w - 2)=16w + 16\), which is equivalent.

Step5: Analyze \((-2w - 2)\cdot(-8)\)

Multiplication is commutative, so \((-2w - 2)\times(-8)=-8\times(-2w - 2)=16w + 16\), which is equivalent.

Answer:

A. \(16w + 16\)
B. \((-6w + 4w - 2)\cdot -8\)
C. \(-8(-8w + 6w - 2)\)
D. \((-2w - 2)\cdot -8\)