Question

write equivalent expressions. use the distributive property to write an equivalent expression. $13 - 8(2x - 6)$ $= 13 + -8(2x + -6)$ $= 13 + (\square \cdot \square) + (\square \cdot \square)$

Explanation:

Step1: Recall Distributive Property

The distributive property is \(a(b + c)=ab+ac\). Here, we have \(-8(2x + (-6))\), so we distribute \(-8\) to \(2x\) and \(-6\).

Step2: Apply Distributive Property

For \(-8(2x + (-6))\), distributing \(-8\) gives \((-8)\cdot(2x)+(-8)\cdot(-6)\). So the expression \(13 + -8(2x + -6)\) becomes \(13+(-8\cdot2x)+(-8\cdot -6)\), and in the boxed form for the middle part, it's \(13 + (\boldsymbol{-8}\cdot\boldsymbol{2x})+(\boldsymbol{-8}\cdot\boldsymbol{-6})\) (but following the box structure in the problem, the first two boxes for the first product are \(-8\) and \(2x\), and the next two are \(-8\) and \(-6\)).

Answer:

The first two boxes (for the first product) are \(-8\) and \(2x\), and the next two boxes (for the second product) are \(-8\) and \(-6\). So filling in the boxes: \(13 + (\boldsymbol{-8}\cdot\boldsymbol{2x})+(\boldsymbol{-8}\cdot\boldsymbol{-6})\) (the boxes should be filled as \(-8\), \(2x\), \(-8\), \(-6\) in order).