Question

1. which expression is equivalent to 4(2x + 3y) - (2y - 3x)?

Explanation:

Step1: Distribute the 4

First, we distribute the 4 in \(4(2x + 3y)\). Using the distributive property \(a(b + c)=ab+ac\), we get \(4\times2x+4\times3y = 8x+12y\).

Step2: Distribute the negative sign

Next, we distribute the negative sign in \(-(2y - 3x)\). This gives us \(-2y+3x\) (because \(-(a - b)=-a + b\)).

Step3: Combine like terms

Now we combine the two results: \((8x+12y)+(-2y + 3x)\). Combining the \(x\)-terms: \(8x+3x = 11x\). Combining the \(y\)-terms: \(12y-2y = 10y\). So the equivalent expression is \(11x + 10y\).

Answer:

\(11x + 10y\)