Basic Math Examples

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

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

Step 1

Factor

b + c

$b + c$ out of

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

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

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Step 1.1

Factor

b + c

$b + c$ out of

a^{2} (b + c)

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

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

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

Step 1.2

Factor

b + c

$b + c$ out of

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

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

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

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

Step 1.3

Factor

b + c

$b + c$ out of

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

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

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

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

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

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

a = a

$a = a$ and

b = b + c

$b = b + c$ .

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

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

Step 3.1.2

Apply the distributive property.

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

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

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

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

Step 3.2

Remove unnecessary parentheses.

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

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

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

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