Basic Math Examples

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

Step 1

Factor

$b + c$ out of

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

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Step 1.1

Factor

$b + c$ out of

$a^{2} (b + c)$ .

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

Step 1.2

Factor

$b + c$ out of

$- {(b + c)}^{3}$ .

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

Step 1.3

Factor

$b + c$ out of

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

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

Step 2

Since both terms are perfect squares, factor using the difference of squares formula,

$a^{2} - b^{2} = (a + b) (a - b)$ where

$a = a$ and

$b = b + c$ .

$(b + c) ((a + b + c) (a - (b + c)))$

Step 3

Factor.

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Step 3.1

Simplify.

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Step 3.1.1

Remove unnecessary parentheses.

$(b + c) ((a + b + c) (a - (b + c)))$

Step 3.1.2

Apply the distributive property.

$(b + c) ((a + b + c) (a - b - c))$

Step 3.2

Remove unnecessary parentheses.

$(b + c) (a + b + c) (a - b - c)$