Question

use the distributive property to write an equivalent expression.
\\(12x - 3(2x - 5)\\)
\\(= 12x + -3(2x + -5)\\)
\\(= 12x + (\square \cdot \square) + (\square \cdot \square)\\)

Explanation:

Step1: Recall distributive property

The distributive property is \(a(b + c)=ab+ac\). Here, we have \(-3(2x + (-5))\), so we distribute \(-3\) to both \(2x\) and \(-5\).

Step2: Apply distributive property

For \(-3(2x + (-5))\), using the distributive property \(a(b + c)=ab + ac\) where \(a=-3\), \(b = 2x\), and \(c=-5\), we get \((-3)\cdot(2x)+(-3)\cdot(-5)\). So the expression \(12x+(-3)(2x + (-5))\) becomes \(12x+((-3)\cdot(2x))+((-3)\cdot(-5))\).

Answer:

The first box is \(-3\), the second is \(2x\), the third is \(-3\), and the fourth is \(-5\) (in order of the boxes from left to right in the two products). So filling in the boxes: \(12x+(\boldsymbol{-3}\cdot\boldsymbol{2x})+(\boldsymbol{-3}\cdot\boldsymbol{-5})\)