How do you factor by grouping #2x^3 + 4x^2 y - 2x^2 - 4xy#?

Answer 1

Notice the similarity of the coefficients, 2, 4, -2, -4. It prompts to group the four terms of this expression into two groups: Group 1: #2x^3+4x^2y# Group 2: #-2x^2-4xy#

Factor out #2x^2# in the first group, getting #2x^2(x+2y)# Factor out #-2x# in the second group, getting #-2x(x+2y)#

Now you see that #(x+2y)# is a common factor in both groups. Therefore, the original expression can be represented as: #2x^2(x+2y)-2x(x+2y)=(2x^2-2x)(x+y)=2x(x-1)(x+2y)#

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Answer 2

Eva Abramson

To factor by grouping 2x^3 + 4x^2 y - 2x^2 - 4xy:

Group the first two terms and the last two terms:

2x^3 + 4x^2 y - 2x^2 - 4xy

Factor out the greatest common factor from each pair of terms:

2x^2(x + 2y) - 2(x + 2y)

Now, factor out the common binomial factor (x + 2y):

2x^2(x + 2y) - 2(x + 2y)

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

= (x + 2y) * 2(x^2 - 1)

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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.