Algebra Examples

$7 x^{2} - 21 x y - 28 y^{2}$

Step 1

Factor $7$ out of $7 x^{2} - 21 x y - 28 y^{2}$ .

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Step 1.1

Factor $7$ out of $7 x^{2}$ .

$7 (x^{2}) - 21 x y - 28 y^{2}$

Step 1.2

Factor $7$ out of $- 21 x y$ .

$7 (x^{2}) + 7 (- 3 x y) - 28 y^{2}$

Step 1.3

Factor $7$ out of $- 28 y^{2}$ .

$7 (x^{2}) + 7 (- 3 x y) + 7 (- 4 y^{2})$

Step 1.4

Factor $7$ out of $7 (x^{2}) + 7 (- 3 x y)$ .

$7 (x^{2} - 3 x y) + 7 (- 4 y^{2})$

Step 1.5

Factor $7$ out of $7 (x^{2} - 3 x y) + 7 (- 4 y^{2})$ .

$7 (x^{2} - 3 x y - 4 y^{2})$

Step 2

Factor.

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Step 2.1

Factor by grouping.

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Step 2.1.1

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 $a \cdot c = 1 \cdot - 4 = - 4$ and whose sum is $b = - 3$ .

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Step 2.1.1.1

Reorder terms.

$7 (x^{2} - 4 y^{2} - 3 x y)$

Step 2.1.1.2

Reorder $- 4 y^{2}$ and $- 3 x y$ .

$7 (x^{2} - 3 x y - 4 y^{2})$

Step 2.1.1.3

Factor $- 3$ out of $- 3 x y$ .

$7 (x^{2} - 3 (x y) - 4 y^{2})$

Step 2.1.1.4

Rewrite $- 3$ as $1$ plus $- 4$

$7 (x^{2} + (1 - 4) (x y) - 4 y^{2})$

Step 2.1.1.5

Apply the distributive property.

$7 (x^{2} + 1 (x y) - 4 (x y) - 4 y^{2})$

Step 2.1.1.6

Multiply $x y$ by $1$ .

$7 (x^{2} + x y - 4 (x y) - 4 y^{2})$

Step 2.1.1.7

Remove unnecessary parentheses.

$7 (x^{2} + x y - 4 x y - 4 y^{2})$

Step 2.1.2

Factor out the greatest common factor from each group.

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Step 2.1.2.1

Group the first two terms and the last two terms.

$7 ((x^{2} + x y) - 4 x y - 4 y^{2})$

Step 2.1.2.2

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

$7 (x (x + y) - 4 y (x + y))$

Step 2.1.3

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

$7 ((x + y) (x - 4 y))$

Step 2.2

Remove unnecessary parentheses.

$7 (x + y) (x - 4 y)$