Algebra Examples

$28 x y - 44 y^{2} + 35 x - 23 y + 40$

Step 1

Regroup terms.

$28 x y + 35 x - 44 y^{2} - 23 y + 40$

Step 2

Factor $7 x$ out of $28 x y + 35 x$ .

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Step 2.1

Factor $7 x$ out of $28 x y$ .

$7 x (4 y) + 35 x - 44 y^{2} - 23 y + 40$

Step 2.2

Factor $7 x$ out of $35 x$ .

$7 x (4 y) + 7 x (5) - 44 y^{2} - 23 y + 40$

Step 2.3

Factor $7 x$ out of $7 x (4 y) + 7 x (5)$ .

$7 x (4 y + 5) - 44 y^{2} - 23 y + 40$

Step 3

Factor by grouping.

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Step 3.1

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 $a \cdot c = - 44 \cdot 40 = - 1760$ and whose sum is $b = - 23$ .

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Step 3.1.1

Factor $- 23$ out of $- 23 y$ .

$7 x (4 y + 5) - 44 y^{2} - 23 (y) + 40$

Step 3.1.2

Rewrite $- 23$ as $32$ plus $- 55$

$7 x (4 y + 5) - 44 y^{2} + (32 - 55) y + 40$

Step 3.1.3

Apply the distributive property.

$7 x (4 y + 5) - 44 y^{2} + 32 y - 55 y + 40$

Step 3.2

Factor out the greatest common factor from each group.

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Step 3.2.1

Group the first two terms and the last two terms.

$7 x (4 y + 5) + (- 44 y^{2} + 32 y) - 55 y + 40$

Step 3.2.2

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

$7 x (4 y + 5) + 4 y (- 11 y + 8) + 5 (- 11 y + 8)$

Step 3.3

Factor the polynomial by factoring out the greatest common factor, $- 11 y + 8$ .

$7 x (4 y + 5) + (- 11 y + 8) (4 y + 5)$

Step 4

Factor $4 y + 5$ out of $7 x (4 y + 5) + (- 11 y + 8) (4 y + 5)$ .

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Step 4.1

Factor $4 y + 5$ out of $7 x (4 y + 5)$ .

$(4 y + 5) (7 x) + (- 11 y + 8) (4 y + 5)$

Step 4.2

Factor $4 y + 5$ out of $(- 11 y + 8) (4 y + 5)$ .

$(4 y + 5) (7 x) + (4 y + 5) (- 11 y + 8)$

Step 4.3

Factor $4 y + 5$ out of $(4 y + 5) (7 x) + (4 y + 5) (- 11 y + 8)$ .

$(4 y + 5) (7 x - 11 y + 8)$