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

Dec 27, 2017

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

$- {q}^{3} {w}^{3} + 8 {q}^{2} {w}^{2} - 35 {q}^{2} {w}^{4} - 27$

#### 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)