Question

How do you combine like terms in `2g ( g + 5) - g ( 5g + 3)`?

Answer 1

`-3g^2+7g`

Explanation:

First we open the brackets and simplify by multiplying the contents of the brackets with the term preceding them. Keep in mind that the product of a negative and a positive is a negative.

`2g(g+5)-g(5g+3)`

`2g^2+10g-5g^2-3g`

Sort so that the like terms with their preceding signs are near each other, and then simplify.

`2g^2-5g^2+10g-3g`

`-3g^2+7g`

Answer 2

See a solution process below:

Explanation:

First, expand the terms in parenthesis by multiplying the terms within the parenthesis by the term outside the parenthesis:

`color(red)(2g)(g + 5) - color(blue)(g)(5g + 3) =>`

`(color(red)(2g) xx g) + (color(red)(2g) xx 5) - (color(blue)(g) xx 5g) - (color(blue)(g) xx 3) =>`

`2g^2 + 10g - 5g^2 - 3g`

Next, group like terms:

`2g^2 - 5g^2 + 10g - 3g`

Now, combine like terms:

`(2 - 5)g^2 + (10 - 3)g`

`-3g^2 + 7g`