Question

How do you simplify `-5q^2w^3(4q+7w)+4qw^2(7q^2w+2q)-3qw(3q^2w^2+9)`?

Answer 1

1) Clear the parentheses by distributing the coefficients.
2) Combine like terms.

Answer:
`-q^3 w^3 + 8 q^2 w^2 - 35 q^2 w^4- 27`

Explanation:

1) Clear the parentheses by distributing the coefficients
Until you have distributed, you can't really see
what the terms actually are.

Distributing one term at a time gives you this:

First term
`−5 q^2 w^3 (4q+7w)`

Distribute the coefficient to get this
`color(blue)(-20 q^3 w^3)- 35 q^2 w^4`

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

Second term
`+4 q w^2 (7 q^2 w+2 q)`

Distribute the coefficient to get this
`color(blue)(+ 28 q^3 w^3) + 8  q^2 w^2`

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

Third term
`−3 q w (3 q^2 w^2+9)`

Distribute the coefficient to get this
`color(blue)(- 9 q^3 w^3) - 27  q w`

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

2) Combine like terms

Put the terms together by first grouping these three like terms
`color(blue)((-20 q^3 w^3 + 28 q^3 w^3 - 9 q^3 w^3))`

These like terms add up like this
`-q^3 w^3`

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

Now you can write the entire expression

`-q^3 w^3 + 8 q^2 w^2 - 35 q^2 w^4 - 27 q w`

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

You can factor this a little if you want, but I don't know if you'd consider that
more or less simplified

`qw("-" q^2w^2 +8qw - 35qw^3 - 27)`