Basic Math Examples

$3 {(c + b)}^{3} - 21 {(c + b)}^{2} - 6 {(c + b)}^{4}$

Step 1

Factor $- 3 {(b + c)}^{2}$ out of $3 {(c + b)}^{3} - 21 {(c + b)}^{2} - 6 {(c + b)}^{4}$ .

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Step 1.1

Reorder the expression.

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Step 1.1.1

Reorder $c$ and $b$ .

$3 {(b + c)}^{3} - 21 {(c + b)}^{2} - 6 {(c + b)}^{4}$

Step 1.1.2

Reorder $c$ and $b$ .

$3 {(b + c)}^{3} - 21 {(b + c)}^{2} - 6 {(c + b)}^{4}$

Step 1.1.3

Reorder $c$ and $b$ .

$3 {(b + c)}^{3} - 21 {(b + c)}^{2} - 6 {(b + c)}^{4}$

Step 1.1.4

Move $- 21 {(b + c)}^{2}$ .

$3 {(b + c)}^{3} - 6 {(b + c)}^{4} - 21 {(b + c)}^{2}$

Step 1.1.5

Reorder $3 {(b + c)}^{3}$ and $- 6 {(b + c)}^{4}$ .

$- 6 {(b + c)}^{4} + 3 {(b + c)}^{3} - 21 {(b + c)}^{2}$

Step 1.2

Factor $- 3 {(b + c)}^{2}$ out of $- 6 {(b + c)}^{4}$ .

$- 3 {(b + c)}^{2} (2 {(b + c)}^{2}) + 3 {(b + c)}^{3} - 21 {(b + c)}^{2}$

Step 1.3

Factor $- 3 {(b + c)}^{2}$ out of $3 {(b + c)}^{3}$ .

$- 3 {(b + c)}^{2} (2 {(b + c)}^{2}) - 3 {(b + c)}^{2} (- (b + c)) - 21 {(b + c)}^{2}$

Step 1.4

Factor $- 3 {(b + c)}^{2}$ out of $- 21 {(b + c)}^{2}$ .

$- 3 {(b + c)}^{2} (2 {(b + c)}^{2}) - 3 {(b + c)}^{2} (- (b + c)) - 3 {(b + c)}^{2} (7)$

Step 1.5

Factor $- 3 {(b + c)}^{2}$ out of $- 3 {(b + c)}^{2} (2 {(b + c)}^{2}) - 3 {(b + c)}^{2} (- (b + c))$ .

$- 3 {(b + c)}^{2} (2 {(b + c)}^{2} - (b + c)) - 3 {(b + c)}^{2} (7)$

Step 1.6

Factor $- 3 {(b + c)}^{2}$ out of $- 3 {(b + c)}^{2} (2 {(b + c)}^{2} - (b + c)) - 3 {(b + c)}^{2} (7)$ .

$- 3 {(b + c)}^{2} (2 {(b + c)}^{2} - (b + c) + 7)$

Step 2

Rewrite ${(b + c)}^{2}$ as $(b + c) (b + c)$ .

$- 3 {(b + c)}^{2} (2 ((b + c) (b + c)) - (b + c) + 7)$

Step 3

Expand $(b + c) (b + c)$ using the FOIL Method.

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Step 3.1

Apply the distributive property.

$- 3 {(b + c)}^{2} (2 (b (b + c) + c (b + c)) - (b + c) + 7)$

Step 3.2

Apply the distributive property.

$- 3 {(b + c)}^{2} (2 (b \cdot b + b c + c (b + c)) - (b + c) + 7)$

Step 3.3

Apply the distributive property.

$- 3 {(b + c)}^{2} (2 (b \cdot b + b c + c b + c \cdot c) - (b + c) + 7)$

Step 4

Simplify and combine like terms.

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Step 4.1

Simplify each term.

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Step 4.1.1

Multiply $b$ by $b$ .

$- 3 {(b + c)}^{2} (2 (b^{2} + b c + c b + c \cdot c) - (b + c) + 7)$

Step 4.1.2

Multiply $c$ by $c$ .

$- 3 {(b + c)}^{2} (2 (b^{2} + b c + c b + c^{2}) - (b + c) + 7)$

Step 4.2

Add $b c$ and $c b$ .

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Step 4.2.1

Reorder $c$ and $b$ .

$- 3 {(b + c)}^{2} (2 (b^{2} + b c + b c + c^{2}) - (b + c) + 7)$

Step 4.2.2

Add $b c$ and $b c$ .

$- 3 {(b + c)}^{2} (2 (b^{2} + 2 b c + c^{2}) - (b + c) + 7)$

Step 5

Apply the distributive property.

$- 3 {(b + c)}^{2} (2 b^{2} + 2 (2 b c) + 2 c^{2} - (b + c) + 7)$

Step 6

Multiply $2$ by $2$ .

$- 3 {(b + c)}^{2} (2 b^{2} + 4 (b c) + 2 c^{2} - (b + c) + 7)$

Step 7

Remove parentheses.

$- 3 {(b + c)}^{2} (2 b^{2} + 4 b c + 2 c^{2} - (b + c) + 7)$

Step 8

Apply the distributive property.

$- 3 {(b + c)}^{2} (2 b^{2} + 4 b c + 2 c^{2} - b - c + 7)$