Algebra Examples

$x^{2} - 11 x y + 28 y^{2}$

Step 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 $a \cdot c = 1 \cdot 28 = 28$ and whose sum is $b = - 11$ .

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Step 1.1

Reorder terms.

$x^{2} + 28 y^{2} - 11 x y$

Step 1.2

Reorder $28 y^{2}$ and $- 11 x y$ .

$x^{2} - 11 x y + 28 y^{2}$

Step 1.3

Factor $- 11$ out of $- 11 x y$ .

$x^{2} - 11 (x y) + 28 y^{2}$

Step 1.4

Rewrite $- 11$ as $- 4$ plus $- 7$

$x^{2} + (- 4 - 7) (x y) + 28 y^{2}$

Step 1.5

Apply the distributive property.

$x^{2} - 4 (x y) - 7 (x y) + 28 y^{2}$

Step 1.6

Remove unnecessary parentheses.

$x^{2} - 4 x y - 7 (x y) + 28 y^{2}$

Step 1.7

Remove unnecessary parentheses.

$x^{2} - 4 x y - 7 x y + 28 y^{2}$

Step 2

Factor out the greatest common factor from each group.

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Step 2.1

Group the first two terms and the last two terms.

$(x^{2} - 4 x y) - 7 x y + 28 y^{2}$

Step 2.2

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

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

Step 3

Factor the polynomial by factoring out the greatest common factor, $x - 4 y$ .

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