How do you multiply #-2xyz(3x^2+2y^2+z^2-4w^2)#?

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Answer 1 · 2017-05-13T14:05:15

#-6x^3yz -4xy^3z -2xyz^3+8w^2xyz#

Use the distributive law to multiply the factor outside by each of the terms inside the bracket,.

Multiply:
the signs, then the numbers, then add the indices of like bases.

#-2xyz(3x^2+2y^2+z^2-4w^2)#

#-6x^3yz -4xy^3z -2xyz^3+8w^2xyz#

There are four terms in the bracket so there should be four terms in the final answer.

Answer 2 · 2017-05-13T14:55:08

#8w^2xyz-6x^3yz-4xy^3z-2xyz^3#

#-2xyz(color(blue)(3x^2+2y^2+z^2-4w^2))#

#:.=color(blue)(3x^2)(-2xyz)+color(blue)(2y^2)(-2xyz)+color(blue)(z^2)(-2xyz)-color(blue)(4w^2)(-2xyz)#

#:.=(-6x^3yz-4xy^3z-2xyz^2+8w^2xyz)#

#:.=color(blue)(8w^2xyz-6x^3yz-4xy^3z-2xyz^3#