Question

factor by grouping.

1. $-72 + 63x^2 - 14x^3 + 16x$
2. $90y + 70 + 90xy + 70x$
3. $6x^3y + 4xy^2 + 54x^2y^2 + 36y^3$

Explanation:

Problem 1: $-72 + 63x^2 - 14x^3 + 16x$

Step1: Rearrange terms by degree

$-14x^3 + 63x^2 + 16x - 72$

Step2: Group into two pairs

$(-14x^3 + 63x^2) + (16x - 72)$

Step3: Factor GCF from each group

$-7x^2(2x - 9) + 8(2x - 9)$

Step4: Factor out common binomial

$(2x - 9)(-7x^2 + 8)$ or $-(2x - 9)(7x^2 - 8)$

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Problem 2: $90y + 70 + 90xy + 70x$

Step1: Rearrange terms

$90xy + 90y + 70x + 70$

Step2: Group into two pairs

$(90xy + 90y) + (70x + 70)$

Step3: Factor GCF from each group

$90y(x + 1) + 70(x + 1)$

Step4: Factor out common binomial

$(x + 1)(90y + 70) = 10(x + 1)(9y + 7)$

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Problem 3: $6x^3y + 4xy^2 + 54x^2y^2 + 36y^3$

Step1: Rearrange terms

$6x^3y + 54x^2y^2 + 4xy^2 + 36y^3$

Step2: Group into two pairs

$(6x^3y + 54x^2y^2) + (4xy^2 + 36y^3)$

Step3: Factor GCF from each group

$6x^2y(x + 9y) + 4y^2(x + 9y)$

Step4: Factor out common binomial

$(x + 9y)(6x^2y + 4y^2) = 2y(x + 9y)(3x^2 + 2y)$

Answer:

1. $(2x - 9)(-7x^2 + 8)$ or $-(2x - 9)(7x^2 - 8)$
2. $10(x + 1)(9y + 7)$
3. $2y(x + 9y)(3x^2 + 2y)$