Algebra Examples

$a c^{2} - a d + c^{3} - c d - b c^{2} + b d$

Step 1

Regroup terms.

$a c^{2} - a d + c^{3} - c d - b c^{2} + b d$

Step 2

Factor $a$ out of $a c^{2} - a d$ .

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Step 2.1

Factor $a$ out of $a c^{2}$ .

$a (c^{2}) - a d + c^{3} - c d - b c^{2} + b d$

Step 2.2

Factor $a$ out of $- a d$ .

$a (c^{2}) + a (- 1 d) + c^{3} - c d - b c^{2} + b d$

Step 2.3

Factor $a$ out of $a (c^{2}) + a (- 1 d)$ .

$a (c^{2} - 1 d) + c^{3} - c d - b c^{2} + b d$

Step 3

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

$a (c^{2} - d) + c^{3} - c d - b c^{2} + b d$

Step 4

Factor out the greatest common factor from each group.

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Step 4.1

Group the first two terms and the last two terms.

$a (c^{2} - d) + (c^{3} - c d) - b c^{2} + b d$

Step 4.2

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

$a (c^{2} - d) + c (c^{2} - 1 d) - b (c^{2} - 1 d)$

Step 5

Factor the polynomial by factoring out the greatest common factor, $c^{2} - 1 d$ .

$a (c^{2} - d) + (c^{2} - 1 d) (c - b)$

Step 6

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

$a (c^{2} - d) + (c^{2} - d) (c - b)$

Step 7

Factor $c^{2} - d$ out of $a (c^{2} - d) + (c^{2} - d) (c - b)$ .

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Step 7.1

Factor $c^{2} - d$ out of $a (c^{2} - d)$ .

$(c^{2} - d) a + (c^{2} - d) (c - b)$

Step 7.2

Factor $c^{2} - d$ out of $(c^{2} - d) a + (c^{2} - d) (c - b)$ .

$(c^{2} - d) (a + c - b)$