How do you simplify #-5v ^ { 2} w ^ { 3} ( v ^ { 2} - 13v ^ { 2} w ^ { 5} + 9w ^ { 4} ) =#?

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Answer 1 · 2018-01-27T09:28:34

The expanded result is #=-5v^4w^3+65v^4w^8-45v^2w^7#.

Use the distributive property:

#-5v^2w^3(color(red)(v^2)-color(blue)(13v^2w^5)+color(green)(9w^4))#

#=-5v^2w^3*color(red)(v^2)-(-5v^2w^3*color(blue)(13v^2w^5))-5v^2w^3*color(green)(9w^4)#

#=-5v^4w^3+65v^4w^8-45v^2w^7#

Answer 2 · 2018-01-27T09:47:05

#color(blue)(-(5v^4w^3)+(65v^4w^8)-(45v^2w^7)#

Given:

#color(red)(-5v ^ { 2} w ^ { 3} ( v ^ { 2} - 13v ^ { 2} w ^ { 5} + 9w ^ { 4} )#

Distribute #color(red)([-5v ^ { 2} w ^ { 3}]# over the terms in the parentheses in the expression as shown below:

#rArr -(5v^2w^3v^2)+(65v^2w^3v^2w^5)-(45v^2w^3w^4)#

We use the formula : #color(brown)(" "a^m*a^n=a^(m+n)# to simplify

#rArr -(5v^4w^3)+(65v^4w^8)-(45v^2w^7)#