Basic Math Examples

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

Step 1

Factor by grouping.

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Step 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

$a \cdot c = 2 \cdot 1 = 2$ and whose sum is

$b = - 3$ .

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Step 1.1.1

Reorder terms.

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

Step 1.1.2

Reorder

$y^{2}$ and

$- 3 c y$ .

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

Step 1.1.3

Factor

$- 3$ out of

$- 3 c y$ .

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

Step 1.1.4

Rewrite

$- 3$ as

$- 1$ plus

$- 2$

$(2 c^{2} + (- 1 - 2) (c y) + y^{2}) (c^{2} + 4 c y - 3 y^{2})$

Step 1.1.5

Apply the distributive property.

$(2 c^{2} - 1 (c y) - 2 (c y) + y^{2}) (c^{2} + 4 c y - 3 y^{2})$

Step 1.1.6

Remove unnecessary parentheses.

$(2 c^{2} - 1 c y - 2 (c y) + y^{2}) (c^{2} + 4 c y - 3 y^{2})$

Step 1.1.7

Remove unnecessary parentheses.

$(2 c^{2} - 1 c y - 2 c y + y^{2}) (c^{2} + 4 c y - 3 y^{2})$

Step 1.2

Factor out the greatest common factor from each group.

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Step 1.2.1

Group the first two terms and the last two terms.

$((2 c^{2} - 1 c y) - 2 c y + y^{2}) (c^{2} + 4 c y - 3 y^{2})$

Step 1.2.2

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

$(c (2 c - 1 y) - y (2 c - y)) (c^{2} + 4 c y - 3 y^{2})$

Step 1.3

Factor the polynomial by factoring out the greatest common factor,

$2 c - 1 y$ .

$(2 c - 1 y) (c - y) (c^{2} + 4 c y - 3 y^{2})$

Step 2

Rewrite

$- 1 y$ as

$- y$ .

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