How do you simplify #3p ^ { 2} q ( p^ { 3} q - 2p ^ { 2} q ^ { 2} - 15p q ^ { 3} )#?

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Answer 1 · 2017-10-01T01:37:14

#3p^3q^2(p+3q)(p-5q)#

#3p^2q(p^3q-2p^2q^2-15pq^3)=3p^2q.pq(p^2-2pq-15p^2)#
#=3p^3q^2(p^2+3pq-5pq-15q^2)#
#=3p^3q^2(p+3q)(p-5q)#

Answer 2 · 2017-10-01T09:27:56

#3p^5q^2-6p^4q^3-45p^3q^4#

To simplify in this case means to remove the brackets.

Do this using the distributive law whereby the factor in front is multiplied by each factor inside the bracket:

#3p^2q(color(red)(p^3q)color(blue)(-2p^2q^2)color(green)( -15pq^3))#

#=color(red)(3p^5q^2)color(blue)(-6p^4q^3)color(green)(-45p^3q^4)#

In each case, multiply the numbers and then add the indices of the same variables.