Factor by Grouping 6x^2y+7xy^2+y^3

$6 x^{2} y + 7 x y^{2} + y^{3}$

Step 1

Factor out the GCF of $y$ from $6 x^{2} y + 7 x y^{2} + y^{3}$ .

Factor out the GCF of $y$ from each term in the polynomial.

Factor out the GCF of $y$ from the expression $6 x^{2} y$ .

$y (6 x^{2}) + 7 x y^{2} + y^{3}$

Factor out the GCF of $y$ from the expression $7 x y^{2}$ .

$y (6 x^{2}) + y (7 x y) + y^{3}$

Factor out the GCF of $y$ from the expression $y^{3}$ .

$y (6 x^{2}) + y (7 x y) + y (y^{2})$

Since all the terms share a common factor of $y$ , it can be factored out of each term.

$y (6 x^{2} + 7 x y + y^{2})$

Step 2

Factor by grouping.

For a polynomial of the form $a x^{2} + b x + c$ , rewrite the middle term as a sum of two terms whose product is $a \cdot c = 6 \cdot 1 = 6$ and whose sum is $b = 7$ .

Reorder terms.

$y (6 x^{2} + y^{2} + 7 x y)$

Reorder $y^{2}$ and $7 x y$ .

$y (6 x^{2} + 7 x y + y^{2})$

Factor $7$ out of $7 x y$ .

$y (6 x^{2} + 7 (x y) + y^{2})$

Rewrite $7$ as $1$ plus $6$

$y (6 x^{2} + (1 + 6) (x y) + y^{2})$

Apply the distributive property.

$y (6 x^{2} + 1 (x y) + 6 (x y) + y^{2})$

Multiply $x y$ by $1$ .

$y (6 x^{2} + x y + 6 (x y) + y^{2})$

Remove unnecessary parentheses.

$y (6 x^{2} + x y + 6 x y + y^{2})$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$y ((6 x^{2} + x y) + 6 x y + y^{2})$

Factor out the greatest common factor (GCF) from each group.

$y (x (6 x + y) + y (6 x + y))$

Factor the polynomial by factoring out the greatest common factor, $6 x + y$ .

$y ((6 x + y) (x + y))$

Factor by Grouping 6x^2y+7xy^2+y^3

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