Algebra Examples

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

Step 1

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

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

Step 2

Simplify terms.

Tap for more steps...

Step 2.1

Simplify each term.

Tap for more steps...

Step 2.1.1

Rewrite using the commutative property of multiplication.

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

Step 2.1.2

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

Tap for more steps...

Step 2.1.2.1

Move $x^{2}$ .

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

Step 2.1.2.2

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

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

Step 2.1.2.3

Add $2$ and $2$ .

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

Step 2.1.3

Multiply $2$ by $3$ .

$6 x^{4} + 2 x^{2} (2 x) + 2 x^{2} \cdot - 1 - 3 x (3 x^{2}) - 3 x (2 x) - 3 x \cdot - 1$

Step 2.1.4

Rewrite using the commutative property of multiplication.

$6 x^{4} + 2 \cdot 2 x^{2} x + 2 x^{2} \cdot - 1 - 3 x (3 x^{2}) - 3 x (2 x) - 3 x \cdot - 1$

Step 2.1.5

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

Tap for more steps...

Step 2.1.5.1

Move $x$ .

$6 x^{4} + 2 \cdot 2 (x \cdot x^{2}) + 2 x^{2} \cdot - 1 - 3 x (3 x^{2}) - 3 x (2 x) - 3 x \cdot - 1$

Step 2.1.5.2

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

Tap for more steps...

Step 2.1.5.2.1

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

$6 x^{4} + 2 \cdot 2 (x^{1} x^{2}) + 2 x^{2} \cdot - 1 - 3 x (3 x^{2}) - 3 x (2 x) - 3 x \cdot - 1$

Step 2.1.5.2.2

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

$6 x^{4} + 2 \cdot 2 x^{1 + 2} + 2 x^{2} \cdot - 1 - 3 x (3 x^{2}) - 3 x (2 x) - 3 x \cdot - 1$

Step 2.1.5.3

Add $1$ and $2$ .

$6 x^{4} + 2 \cdot 2 x^{3} + 2 x^{2} \cdot - 1 - 3 x (3 x^{2}) - 3 x (2 x) - 3 x \cdot - 1$

Step 2.1.6

Multiply $2$ by $2$ .

$6 x^{4} + 4 x^{3} + 2 x^{2} \cdot - 1 - 3 x (3 x^{2}) - 3 x (2 x) - 3 x \cdot - 1$

Step 2.1.7

Multiply $- 1$ by $2$ .

$6 x^{4} + 4 x^{3} - 2 x^{2} - 3 x (3 x^{2}) - 3 x (2 x) - 3 x \cdot - 1$

Step 2.1.8

Rewrite using the commutative property of multiplication.

$6 x^{4} + 4 x^{3} - 2 x^{2} - 3 \cdot 3 x \cdot x^{2} - 3 x (2 x) - 3 x \cdot - 1$

Step 2.1.9

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

Tap for more steps...

Step 2.1.9.1

Move $x^{2}$ .

$6 x^{4} + 4 x^{3} - 2 x^{2} - 3 \cdot 3 (x^{2} x) - 3 x (2 x) - 3 x \cdot - 1$

Step 2.1.9.2

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

Tap for more steps...

Step 2.1.9.2.1

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

$6 x^{4} + 4 x^{3} - 2 x^{2} - 3 \cdot 3 (x^{2} x^{1}) - 3 x (2 x) - 3 x \cdot - 1$

Step 2.1.9.2.2

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

$6 x^{4} + 4 x^{3} - 2 x^{2} - 3 \cdot 3 x^{2 + 1} - 3 x (2 x) - 3 x \cdot - 1$

Step 2.1.9.3

Add $2$ and $1$ .

$6 x^{4} + 4 x^{3} - 2 x^{2} - 3 \cdot 3 x^{3} - 3 x (2 x) - 3 x \cdot - 1$

Step 2.1.10

Multiply $- 3$ by $3$ .

$6 x^{4} + 4 x^{3} - 2 x^{2} - 9 x^{3} - 3 x (2 x) - 3 x \cdot - 1$

Step 2.1.11

Rewrite using the commutative property of multiplication.

$6 x^{4} + 4 x^{3} - 2 x^{2} - 9 x^{3} - 3 \cdot 2 x \cdot x - 3 x \cdot - 1$

Step 2.1.12

Multiply $x$ by $x$ by adding the exponents.

Tap for more steps...

Step 2.1.12.1

Move $x$ .

$6 x^{4} + 4 x^{3} - 2 x^{2} - 9 x^{3} - 3 \cdot 2 (x \cdot x) - 3 x \cdot - 1$

Step 2.1.12.2

Multiply $x$ by $x$ .

$6 x^{4} + 4 x^{3} - 2 x^{2} - 9 x^{3} - 3 \cdot 2 x^{2} - 3 x \cdot - 1$

Step 2.1.13

Multiply $- 3$ by $2$ .

$6 x^{4} + 4 x^{3} - 2 x^{2} - 9 x^{3} - 6 x^{2} - 3 x \cdot - 1$

Step 2.1.14

Multiply $- 1$ by $- 3$ .

$6 x^{4} + 4 x^{3} - 2 x^{2} - 9 x^{3} - 6 x^{2} + 3 x$

Step 2.2

Simplify by adding terms.

Tap for more steps...

Step 2.2.1

Subtract $9 x^{3}$ from $4 x^{3}$ .

$6 x^{4} - 5 x^{3} - 2 x^{2} - 6 x^{2} + 3 x$

Step 2.2.2

Subtract $6 x^{2}$ from $- 2 x^{2}$ .

$6 x^{4} - 5 x^{3} - 8 x^{2} + 3 x$