Algebra Examples

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

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

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

Step 3

Simplify terms.

Tap for more steps...

Step 3.1

Simplify each term.

Tap for more steps...

Step 3.1.1

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

Tap for more steps...

Step 3.1.1.1

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

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

Step 3.1.1.2

Add $2$ and $2$ .

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

Step 3.1.2

Rewrite using the commutative property of multiplication.

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

Step 3.1.3

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

Tap for more steps...

Step 3.1.3.1

Move $x$ .

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

Step 3.1.3.2

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

Tap for more steps...

Step 3.1.3.2.1

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

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

Step 3.1.3.2.2

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

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

Step 3.1.3.3

Add $1$ and $2$ .

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

Step 3.1.4

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

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

Step 3.1.5

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

Tap for more steps...

Step 3.1.5.1

Move $x^{2}$ .

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

Step 3.1.5.2

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

Tap for more steps...

Step 3.1.5.2.1

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

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

Step 3.1.5.2.2

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

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

Step 3.1.5.3

Add $2$ and $1$ .

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

Step 3.1.6

Rewrite using the commutative property of multiplication.

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

Step 3.1.7

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

Tap for more steps...

Step 3.1.7.1

Move $x$ .

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

Step 3.1.7.2

Multiply $x$ by $x$ .

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

Step 3.1.8

Multiply $- 1$ by $- 1$ .

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

Step 3.1.9

Multiply $x^{2}$ by $1$ .

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

Step 3.1.10

Multiply $- 2$ by $- 1$ .

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

Step 3.1.11

Multiply $- 1$ by $- 2$ .

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

Step 3.1.12

Multiply $- 2$ by $- 2$ .

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

Step 3.2

Simplify by adding terms.

Tap for more steps...

Step 3.2.1

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

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

Step 3.2.2

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

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

Step 3.2.3

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

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

Step 3.2.4

Add $2 x$ and $2 x$ .

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