Rename each of the following using the distributive property of multiplication over addition:

A: ax+ bx+ 2x
B: 3(a+b)+ x(a+b)

and explain how you got this answer please!

x (a + b +2) distributive of multipication

(x+3)(a+b) distributive again and I also used commutative to make 3+x --> (x+3)

x(a+b+2)

(x+3)(a+b)

To rename each of the given expressions using the distributive property of multiplication over addition, we need to multiply each term individually by the values outside the parentheses.

Let's start with expression A:
A: ax + bx + 2x

To use the distributive property, we multiply each term inside the parentheses by the values outside the parentheses:

ax + bx + 2x = (a + b + 2) * x

We simply distributed the x to each term inside the parentheses.

Now, let's move on to expression B:
B: 3(a + b) + x(a + b)

To apply the distributive property, we multiply each term inside the parentheses by the values outside the parentheses:

3(a + b) + x(a + b) = (3 + x) * (a + b)

Again, we distributed the values outside the parentheses (3 and x) to each term inside the parentheses.

So, the renamed expressions are:
A: (a + b + 2) * x
B: (3 + x) * (a + b)

This is how we utilize the distributive property of multiplication over addition to rename the given expressions.