How do you factor #2x^2 (x + y) - y(x + y)^2#?

Answer 1

#(x+y)(x-y)(2x+y)#

#"take out a "color(blue)"common factor "(x+y)#
#=(x+y)[2x^2-y(x+y)]#
#=(x+y)[2x^2-xy-y^2]#
#"factorise "2x^2-xy-y^2" using the a-c method"#
#"the factors of the product "2xx-1=-2#
#"which sum to - 1 are - 2 and + 1"#
#"split the middle term using these factors"#
#2x^2-2xy+xy-y^2larrcolor(blue)"factor by grouping"#
#=color(red)(2x)(x-y)color(red)(+y)(x-y)#
#"take out the "color(blue)"common factor "(x-y)#
#=(x-y)(color(red)(2x+y))#
#rArr2x^2(x+y)-y(x+y)^2=(x+y(x-y)(2x+y)#
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Answer 2

To factor (2x^2 (x + y) - y(x + y)^2), first, notice that both terms have a common factor of ((x + y)).

Factor out ((x + y)) from both terms:

[2x^2 (x + y) - y(x + y)^2 = (x + y)(2x^2 - y(x + y))]

Then, further simplify the expression inside the parentheses:

[2x^2 - y(x + y) = 2x^2 - yx - y^2]

So, the factored form of (2x^2 (x + y) - y(x + y)^2) is ((x + y)(2x^2 - yx - y^2)).

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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.

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.

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.

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.

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