Algebra Examples

$(3 x + 2) (2 x^{2} + 6 x - 3)$

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 $(3 x + 2) (2 x^{2} + 6 x - 3)$ by multiplying each term in the first expression by each term in the second expression.

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

Step 3

Simplify terms.

Tap for more steps...

Step 3.1

Simplify each term.

Tap for more steps...

Step 3.1.1

Rewrite using the commutative property of multiplication.

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

Step 3.1.2

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

Tap for more steps...

Step 3.1.2.1

Move $x^{2}$ .

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

Step 3.1.2.2

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

Tap for more steps...

Step 3.1.2.2.1

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

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

Step 3.1.2.2.2

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

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

Step 3.1.2.3

Add $2$ and $1$ .

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

Step 3.1.3

Multiply $3$ by $2$ .

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

Step 3.1.4

Rewrite using the commutative property of multiplication.

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

Step 3.1.5

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

Tap for more steps...

Step 3.1.5.1

Move $x$ .

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

Step 3.1.5.2

Multiply $x$ by $x$ .

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

Step 3.1.6

Multiply $3$ by $6$ .

$6 x^{3} + 18 x^{2} + 3 x \cdot - 3 + 2 (2 x^{2}) + 2 (6 x) + 2 \cdot - 3$

Step 3.1.7

Multiply $- 3$ by $3$ .

$6 x^{3} + 18 x^{2} - 9 x + 2 (2 x^{2}) + 2 (6 x) + 2 \cdot - 3$

Step 3.1.8

Multiply $2$ by $2$ .

$6 x^{3} + 18 x^{2} - 9 x + 4 x^{2} + 2 (6 x) + 2 \cdot - 3$

Step 3.1.9

Multiply $6$ by $2$ .

$6 x^{3} + 18 x^{2} - 9 x + 4 x^{2} + 12 x + 2 \cdot - 3$

Step 3.1.10

Multiply $2$ by $- 3$ .

$6 x^{3} + 18 x^{2} - 9 x + 4 x^{2} + 12 x - 6$

Step 3.2

Simplify by adding terms.

Tap for more steps...

Step 3.2.1

Add $18 x^{2}$ and $4 x^{2}$ .

$6 x^{3} + 22 x^{2} - 9 x + 12 x - 6$

Step 3.2.2

Add $- 9 x$ and $12 x$ .

$6 x^{3} + 22 x^{2} + 3 x - 6$