Algebra Examples

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

Step 1

To write a polynomial in standard form, simplify and then arrange the terms in descending order.

$a x^{2} + b x + c$

Step 2

Expand $(3 + b^{2}) (3 - b^{2})$ using the FOIL Method.

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Step 2.1

Apply the distributive property.

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

Step 2.2

Apply the distributive property.

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

Step 2.3

Apply the distributive property.

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

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 $3$ by $3$ .

$9 + 3 (- b^{2}) + b^{2} \cdot 3 + b^{2} (- b^{2})$

Step 3.1.2

Multiply $- 1$ by $3$ .

$9 - 3 b^{2} + b^{2} \cdot 3 + b^{2} (- b^{2})$

Step 3.1.3

Move $3$ to the left of $b^{2}$ .

$9 - 3 b^{2} + 3 \cdot b^{2} + b^{2} (- b^{2})$

Step 3.1.4

Rewrite using the commutative property of multiplication.

$9 - 3 b^{2} + 3 b^{2} - b^{2} b^{2}$

Step 3.1.5

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

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Step 3.1.5.1

Move $b^{2}$ .

$9 - 3 b^{2} + 3 b^{2} - (b^{2} b^{2})$

Step 3.1.5.2

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

$9 - 3 b^{2} + 3 b^{2} - b^{2 + 2}$

Step 3.1.5.3

Add $2$ and $2$ .

$9 - 3 b^{2} + 3 b^{2} - b^{4}$

Step 3.2

Add $- 3 b^{2}$ and $3 b^{2}$ .

$9 + 0 - b^{4}$

Step 3.3

Add $9$ and $0$ .

$9 - b^{4}$

Step 4

Reorder $9$ and $- b^{4}$ .

$- b^{4} + 9$