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

Answer 1

Avery Alexander

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

Multiply the factor outside by each of the terms inside the bracket using the distributive law.

First multiply the signs, then the numbers, and lastly add the like-base indices.

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

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

Since there are four terms in the bracket, the final answer should also contain four terms.

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Answer 2

Savannah Anderson

#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#

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.