Algebra Examples

$(x^{3} - x^{2}) (x^{2} + 3 x + 1)$

Step 1

Expand $(x^{3} - x^{2}) (x^{2} + 3 x + 1)$ by multiplying each term in the first expression by each term in the second expression.

$x^{3} x^{2} + x^{3} (3 x) + x^{3} \cdot 1 - x^{2} x^{2} - x^{2} (3 x) - x^{2} \cdot 1$

Step 2

Simplify terms.

Tap for more steps...

Step 2.1

Simplify each term.

Tap for more steps...

Step 2.1.1

Multiply $x^{3}$ by $x^{2}$ by adding the exponents.

Tap for more steps...

Step 2.1.1.1

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

$x^{3 + 2} + x^{3} (3 x) + x^{3} \cdot 1 - x^{2} x^{2} - x^{2} (3 x) - x^{2} \cdot 1$

Step 2.1.1.2

Add $3$ and $2$ .

$x^{5} + x^{3} (3 x) + x^{3} \cdot 1 - x^{2} x^{2} - x^{2} (3 x) - x^{2} \cdot 1$

Step 2.1.2

Rewrite using the commutative property of multiplication.

$x^{5} + 3 x^{3} x + x^{3} \cdot 1 - x^{2} x^{2} - x^{2} (3 x) - x^{2} \cdot 1$

Step 2.1.3

Multiply $x^{3}$ by $x$ by adding the exponents.

Tap for more steps...

Step 2.1.3.1

Move $x$ .

$x^{5} + 3 (x \cdot x^{3}) + x^{3} \cdot 1 - x^{2} x^{2} - x^{2} (3 x) - x^{2} \cdot 1$

Step 2.1.3.2

Multiply $x$ by $x^{3}$ .

Tap for more steps...

Step 2.1.3.2.1

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

$x^{5} + 3 (x^{1} x^{3}) + x^{3} \cdot 1 - x^{2} x^{2} - x^{2} (3 x) - x^{2} \cdot 1$

Step 2.1.3.2.2

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

$x^{5} + 3 x^{1 + 3} + x^{3} \cdot 1 - x^{2} x^{2} - x^{2} (3 x) - x^{2} \cdot 1$

Step 2.1.3.3

Add $1$ and $3$ .

$x^{5} + 3 x^{4} + x^{3} \cdot 1 - x^{2} x^{2} - x^{2} (3 x) - x^{2} \cdot 1$

Step 2.1.4

Multiply $x^{3}$ by $1$ .

$x^{5} + 3 x^{4} + x^{3} - x^{2} x^{2} - x^{2} (3 x) - x^{2} \cdot 1$

Step 2.1.5

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

Tap for more steps...

Step 2.1.5.1

Move $x^{2}$ .

$x^{5} + 3 x^{4} + x^{3} - (x^{2} x^{2}) - x^{2} (3 x) - x^{2} \cdot 1$

Step 2.1.5.2

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

$x^{5} + 3 x^{4} + x^{3} - x^{2 + 2} - x^{2} (3 x) - x^{2} \cdot 1$

Step 2.1.5.3

Add $2$ and $2$ .

$x^{5} + 3 x^{4} + x^{3} - x^{4} - x^{2} (3 x) - x^{2} \cdot 1$

Step 2.1.6

Rewrite using the commutative property of multiplication.

$x^{5} + 3 x^{4} + x^{3} - x^{4} - 1 \cdot 3 x^{2} x - x^{2} \cdot 1$

Step 2.1.7

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

Tap for more steps...

Step 2.1.7.1

Move $x$ .

$x^{5} + 3 x^{4} + x^{3} - x^{4} - 1 \cdot 3 (x \cdot x^{2}) - x^{2} \cdot 1$

Step 2.1.7.2

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

Tap for more steps...

Step 2.1.7.2.1

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

$x^{5} + 3 x^{4} + x^{3} - x^{4} - 1 \cdot 3 (x^{1} x^{2}) - x^{2} \cdot 1$

Step 2.1.7.2.2

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

$x^{5} + 3 x^{4} + x^{3} - x^{4} - 1 \cdot 3 x^{1 + 2} - x^{2} \cdot 1$

Step 2.1.7.3

Add $1$ and $2$ .

$x^{5} + 3 x^{4} + x^{3} - x^{4} - 1 \cdot 3 x^{3} - x^{2} \cdot 1$

Step 2.1.8

Multiply $- 1$ by $3$ .

$x^{5} + 3 x^{4} + x^{3} - x^{4} - 3 x^{3} - x^{2} \cdot 1$

Step 2.1.9

Multiply $- 1$ by $1$ .

$x^{5} + 3 x^{4} + x^{3} - x^{4} - 3 x^{3} - x^{2}$

Step 2.2

Simplify by adding terms.

Tap for more steps...

Step 2.2.1

Subtract $x^{4}$ from $3 x^{4}$ .

$x^{5} + 2 x^{4} + x^{3} - 3 x^{3} - x^{2}$

Step 2.2.2

Subtract $3 x^{3}$ from $x^{3}$ .

$x^{5} + 2 x^{4} - 2 x^{3} - x^{2}$