Algebra Examples

$16 x^{2} c + 8 x (y d) - 16 x^{2} d - 8 x y c$

Step 1

Remove parentheses.

$16 x^{2} c + 8 x y d - 16 x^{2} d - 8 x y c$

Step 2

Factor $8 x$ out of $16 x^{2} c + 8 x y d - 16 x^{2} d - 8 x y c$ .

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Step 2.1

Factor $8 x$ out of $16 x^{2} c$ .

$8 x (2 x c) + 8 x y d - 16 x^{2} d - 8 x y c$

Step 2.2

Factor $8 x$ out of $8 x y d$ .

$8 x (2 x c) + 8 x (y d) - 16 x^{2} d - 8 x y c$

Step 2.3

Factor $8 x$ out of $- 16 x^{2} d$ .

$8 x (2 x c) + 8 x (y d) + 8 x (- 2 x d) - 8 x y c$

Step 2.4

Factor $8 x$ out of $- 8 x y c$ .

$8 x (2 x c) + 8 x (y d) + 8 x (- 2 x d) + 8 x (- 1 y c)$

Step 2.5

Factor $8 x$ out of $8 x (2 x c) + 8 x (y d)$ .

$8 x (2 x c + y d) + 8 x (- 2 x d) + 8 x (- 1 y c)$

Step 2.6

Factor $8 x$ out of $8 x (2 x c + y d) + 8 x (- 2 x d)$ .

$8 x (2 x c + y d - 2 x d) + 8 x (- 1 y c)$

Step 2.7

Factor $8 x$ out of $8 x (2 x c + y d - 2 x d) + 8 x (- 1 y c)$ .

$8 x (2 x c + y d - 2 x d - 1 y c)$

Step 3

Regroup terms.

$8 x (- 2 x d + 2 x c + y d - 1 y c)$

Step 4

Rewrite $- 1 y$ as $- y$ .

$8 x (- 2 x d + 2 x c + y d - y c)$

Step 5

Factor out the greatest common factor from each group.

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Step 5.1

Group the first two terms and the last two terms.

$8 x ((- 2 x d + 2 x c) + y d - y c)$

Step 5.2

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

$8 x (2 x (- 1 d + c) - y (- 1 d + c))$

Step 6

Factor the polynomial by factoring out the greatest common factor, $- 1 d + c$ .

$8 x ((- 1 d + c) (2 x - y))$

Step 7

Factor.

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Step 7.1

Rewrite $- 1 d$ as $- d$ .

$8 x ((- d + c) (2 x - y))$

Step 7.2

Remove unnecessary parentheses.

$8 x (- d + c) (2 x - y)$

Step 8

Factor.

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Step 8.1

Factor $- 1$ out of $- d + c$ .

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Step 8.1.1

Reorder $- d$ and $c$ .

$8 x (c - d) (2 x - y)$

Step 8.1.2

Factor $- 1$ out of $c$ .

$8 x (- 1 (- c) - d) (2 x - y)$

Step 8.1.3

Factor $- 1$ out of $- d$ .

$8 x (- 1 (- c) - (d)) (2 x - y)$

Step 8.1.4

Factor $- 1$ out of $- 1 (- c) - (d)$ .

$8 x (- 1 (- c + d)) (2 x - y)$

Step 8.1.5

Rewrite $- 1 (- c + d)$ as $- (- c + d)$ .

$8 x (- (- c + d)) (2 x - y)$

Step 8.2

Remove unnecessary parentheses.

$8 x \cdot - 1 (- c + d) (2 x - y)$

Step 9

Factor.

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Step 9.1

Combine exponents.

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Step 9.1.1

Factor out negative.

$- ((8 x (- c + d)) (2 x - y))$

Step 9.1.2

Multiply $8$ by $- 1$ .

$- 8 ((x (- c + d)) (2 x - y))$

Step 9.2

Remove unnecessary parentheses.

$- 8 x (- c + d) (2 x - y)$

Step 10

Factor.

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Step 10.1

Factor $- 1$ out of $- c + d$ .

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Step 10.1.1

Factor $- 1$ out of $- c$ .

$- 8 x (- (c) + d) (2 x - y)$

Step 10.1.2

Factor $- 1$ out of $d$ .

$- 8 x (- (c) - 1 (- d)) (2 x - y)$

Step 10.1.3

Factor $- 1$ out of $- (c) - 1 (- d)$ .

$- 8 x (- (c - d)) (2 x - y)$

Step 10.2

Remove unnecessary parentheses.

$- 8 x \cdot - 1 (c - d) (2 x - y)$

Step 11

Factor.

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Step 11.1

Combine exponents.

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Step 11.1.1

Factor out negative.

$- ((- 8 x (c - d)) (2 x - y))$

Step 11.1.2

Multiply $- 8$ by $- 1$ .

$8 ((x (c - d)) (2 x - y))$

Step 11.2

Remove unnecessary parentheses.

$8 x (c - d) (2 x - y)$