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

1 Answer
Dec 27, 2017

Answer:

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)#