Algebra Examples

$(x - 1) (x + 2) (2 x + 2)$

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 $(x - 1) (x + 2)$ using the FOIL Method.

Tap for more steps...

Step 2.1

Apply the distributive property.

$(x (x + 2) - 1 (x + 2)) (2 x + 2)$

Step 2.2

Apply the distributive property.

$(x \cdot x + x \cdot 2 - 1 (x + 2)) (2 x + 2)$

Step 2.3

Apply the distributive property.

$(x \cdot x + x \cdot 2 - 1 x - 1 \cdot 2) (2 x + 2)$

Step 3

Simplify and combine like terms.

Tap for more steps...

Step 3.1

Simplify each term.

Tap for more steps...

Step 3.1.1

Multiply $x$ by $x$ .

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

Step 3.1.2

Move $2$ to the left of $x$ .

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

Step 3.1.3

Rewrite $- 1 x$ as $- x$ .

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

Step 3.1.4

Multiply $- 1$ by $2$ .

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

Step 3.2

Subtract $x$ from $2 x$ .

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

Step 4

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

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

Step 5

Simplify terms.

Tap for more steps...

Step 5.1

Simplify each term.

Tap for more steps...

Step 5.1.1

Rewrite using the commutative property of multiplication.

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

Step 5.1.2

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

Tap for more steps...

Step 5.1.2.1

Move $x$ .

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

Step 5.1.2.2

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

Tap for more steps...

Step 5.1.2.2.1

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

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

Step 5.1.2.2.2

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

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

Step 5.1.2.3

Add $1$ and $2$ .

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

Step 5.1.3

Move $2$ to the left of $x^{2}$ .

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

Step 5.1.4

Rewrite using the commutative property of multiplication.

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

Step 5.1.5

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

Tap for more steps...

Step 5.1.5.1

Move $x$ .

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

Step 5.1.5.2

Multiply $x$ by $x$ .

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

Step 5.1.6

Move $2$ to the left of $x$ .

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

Step 5.1.7

Multiply $2$ by $- 2$ .

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

Step 5.1.8

Multiply $- 2$ by $2$ .

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

Step 5.2

Simplify by adding terms.

Tap for more steps...

Step 5.2.1

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

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

Step 5.2.2

Subtract $4 x$ from $2 x$ .

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