How do you find the product #-3p^4r^3(2p^2r^4-6p^6r^3-5)#?

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Answer 1 · 2017-04-12T07:35:31

#-6p^6r^7 + 18p^10r^6 + 15p^4r^3#

First distribute. Make sure to distribute the negative signs correctly:

#-3p^4r^3(2p^2r^4 - 6p^6r^3 - 5) #

#= (-3)(2)p^4p^2r^3r^4 + (-3)(-6)p^4p^6r^3r^3 + (-3)(-5)p^4r^3#

Multiply the constants:

#= -6p^4p^2r^3r^4 +18p^4p^6r^3r^3 + 15p^4r^3#

Use the exponent rule #x^m x^n = x^(m+n)# to add the exponents of like variables:

#= -6 p^(4+2) r^(3+4) + 18 p^(4+6) r^(3+3) + 15 p^4r^3#

#= -6 p^6 r^7 + 18 p^10 r^6 + 15 p^4 r^3#