Algebra Examples

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

Step 1

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

Tap for more steps...

Step 1.1

Apply the distributive property.

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

Step 1.2

Apply the distributive property.

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

Step 1.3

Apply the distributive property.

$a^{2} a + a^{2} b^{2} + b a + b \cdot b^{2}$

Step 2

Simplify terms.

Tap for more steps...

Step 2.1

Simplify each term.

Tap for more steps...

Step 2.1.1

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

Tap for more steps...

Step 2.1.1.1

Multiply $a^{2}$ by $a$ .

Tap for more steps...

Step 2.1.1.1.1

Raise $a$ to the power of $1$ .

$a^{2} a^{1} + a^{2} b^{2} + b a + b \cdot b^{2}$

Step 2.1.1.1.2

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

$a^{2 + 1} + a^{2} b^{2} + b a + b \cdot b^{2}$

Step 2.1.1.2

Add $2$ and $1$ .

$a^{3} + a^{2} b^{2} + b a + b \cdot b^{2}$

Step 2.1.2

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

Tap for more steps...

Step 2.1.2.1

Multiply $b$ by $b^{2}$ .

Tap for more steps...

Step 2.1.2.1.1

Raise $b$ to the power of $1$ .

$a^{3} + a^{2} b^{2} + b a + b^{1} b^{2}$

Step 2.1.2.1.2

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

$a^{3} + a^{2} b^{2} + b a + b^{1 + 2}$

Step 2.1.2.2

Add $1$ and $2$ .

$a^{3} + a^{2} b^{2} + b a + b^{3}$

Step 2.2

Simplify the expression.

Tap for more steps...

Step 2.2.1

Reorder $b$ and $a$ .

$a^{3} + a^{2} b^{2} + a b + b^{3}$

Step 2.2.2

Move $a b$ .

$a^{3} + a^{2} b^{2} + b^{3} + a b$

Step 2.2.3

Reorder $a^{3}$ and $a^{2} b^{2}$ .

$a^{2} b^{2} + a^{3} + b^{3} + a b$