Question

How do you combine like terms in `3( 2a - b ) - 7( 3b - 5a )`?

Answer 1

`41a - 5b`

Explanation:

Before we combine like terms, we first use the distributive property, as shown here:

Following this image, we can distribute/expand `color(blue)(3(2a-b))` and `color(blue)(-7(3b-5a))`.

`color(blue)(3(2a-b) = 6a - 3b)`

`color(blue)(-7(3b-5a) = -21b + 35a)`

Now put these back into the expression:
`6a - 3b - 21b + 35a`

Now let's color-code the like terms:
`color(red)(6a) quadcolor(green)(-quad3b) quadcolor(green)(-quad2b) quadcolor(red)(+quad35a)`

Combine like terms:
`41a - 5b`

Hope this helps!