Basic Math Examples

$(2 - b) (2 + b) (4 + b^{2}) + (1 + b^{2})$

Step 1

Remove parentheses.

$(2 - b) (2 + b) (4 + b^{2}) + 1 + b^{2}$

Step 2

Expand $(2 - b) (2 + b)$ using the FOIL Method.

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Step 2.1

Apply the distributive property.

$(2 (2 + b) - b (2 + b)) (4 + b^{2}) + 1 + b^{2}$

Step 2.2

Apply the distributive property.

$(2 \cdot 2 + 2 b - b (2 + b)) (4 + b^{2}) + 1 + b^{2}$

Step 2.3

Apply the distributive property.

$(2 \cdot 2 + 2 b - b \cdot 2 - b \cdot b) (4 + b^{2}) + 1 + b^{2}$

Step 3

Simplify and combine like terms.

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Step 3.1

Simplify each term.

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Step 3.1.1

Multiply $2$ by $2$ .

$(4 + 2 b - b \cdot 2 - b \cdot b) (4 + b^{2}) + 1 + b^{2}$

Step 3.1.2

Multiply $2$ by $- 1$ .

$(4 + 2 b - 2 b - b \cdot b) (4 + b^{2}) + 1 + b^{2}$

Step 3.1.3

Multiply $b$ by $b$ by adding the exponents.

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Step 3.1.3.1

Move $b$ .

$(4 + 2 b - 2 b - (b \cdot b)) (4 + b^{2}) + 1 + b^{2}$

Step 3.1.3.2

Multiply $b$ by $b$ .

$(4 + 2 b - 2 b - b^{2}) (4 + b^{2}) + 1 + b^{2}$

Step 3.2

Subtract $2 b$ from $2 b$ .

$(4 + 0 - b^{2}) (4 + b^{2}) + 1 + b^{2}$

Step 3.3

Add $4$ and $0$ .

$(4 - b^{2}) (4 + b^{2}) + 1 + b^{2}$

Step 4

Expand $(4 - b^{2}) (4 + b^{2})$ using the FOIL Method.

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Step 4.1

Apply the distributive property.

$4 (4 + b^{2}) - b^{2} (4 + b^{2}) + 1 + b^{2}$

Step 4.2

Apply the distributive property.

$4 \cdot 4 + 4 b^{2} - b^{2} (4 + b^{2}) + 1 + b^{2}$

Step 4.3

Apply the distributive property.

$4 \cdot 4 + 4 b^{2} - b^{2} \cdot 4 - b^{2} b^{2} + 1 + b^{2}$

Step 5

Simplify and combine like terms.

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Step 5.1

Simplify each term.

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Step 5.1.1

Multiply $4$ by $4$ .

$16 + 4 b^{2} - b^{2} \cdot 4 - b^{2} b^{2} + 1 + b^{2}$

Step 5.1.2

Multiply $4$ by $- 1$ .

$16 + 4 b^{2} - 4 b^{2} - b^{2} b^{2} + 1 + b^{2}$

Step 5.1.3

Multiply $b^{2}$ by $b^{2}$ by adding the exponents.

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Step 5.1.3.1

Move $b^{2}$ .

$16 + 4 b^{2} - 4 b^{2} - (b^{2} b^{2}) + 1 + b^{2}$

Step 5.1.3.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$16 + 4 b^{2} - 4 b^{2} - b^{2 + 2} + 1 + b^{2}$

Step 5.1.3.3

Add $2$ and $2$ .

$16 + 4 b^{2} - 4 b^{2} - b^{4} + 1 + b^{2}$

Step 5.2

Subtract $4 b^{2}$ from $4 b^{2}$ .

$16 + 0 - b^{4} + 1 + b^{2}$

Step 5.3

Add $16$ and $0$ .

$16 - b^{4} + 1 + b^{2}$

Step 6

Add $16$ and $1$ .

$- b^{4} + 17 + b^{2}$

Step 7

Reorder terms.

$- b^{4} + b^{2} + 17$

Step 8

Factor $- 1$ out of $- b^{4} + b^{2} + 17$ .

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Step 8.1

Factor $- 1$ out of $- b^{4}$ .

$- (b^{4}) + b^{2} + 17$

Step 8.2

Factor $- 1$ out of $b^{2}$ .

$- (b^{4}) - 1 (- b^{2}) + 17$

Step 8.3

Rewrite $17$ as $- 1 (- 17)$ .

$- (b^{4}) - 1 (- b^{2}) - 1 (- 17)$

Step 8.4

Factor $- 1$ out of $- (b^{4}) - 1 (- b^{2})$ .

$- (b^{4} - b^{2}) - 1 (- 17)$

Step 8.5

Factor $- 1$ out of $- (b^{4} - b^{2}) - 1 (- 17)$ .

$- (b^{4} - b^{2} - 17)$