How do you find the product of #(-6x-7y^2)^2#?

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Answer 1 · 2018-04-11T01:49:47

The final product is #36x^2+84xy^2+49y^4#.

First, you can factor out a negative one:

#color(white)=(-6x-7y^2)^2#

#=(-1*(6x+7y^2))^2#

#=(-1)^2*(6x+7y^2)^2#

#=1*(6x+7y^2)^2#

#=(6x+7y^2)^2#

Then, write out the actual multiplication:

#=(6x+7y^2)(6x+7y^2)#

Now, multiply each combination of the factors (called FOIL method):

#=6x*6x+6x*7y^2+7y^2*6x+7y^2*7y^2#

#=36x^2+42xy^2+42xy^2+49y^4#

#=36x^2+84xy^2+49y^4#

That's the product. Hope this helped!

Answer 2 · 2018-04-11T01:59:06

#(-6x-7y^2)^2=color(blue)(36x^2+84xy^2+49y^4#

Given:

#(-6x-7y^2)^2#

Use the square of a difference:

#(a-b)^2=a^2-2ab+b^2#,

where:

#a=-6x#, and #b=7y^2#.

#(-6x-7y^2)^2=#

#(-6x)^2-2(-6x)(7y^2)+(7y^2)^2#

Simplify.

#36x^2+84xy^2+49y^4#