Algebra Examples

$4 (x - 5) (x^{2} + x + 2)$

Step 1

Simplify by multiplying through.

Tap for more steps...

Step 1.1

Apply the distributive property.

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

Step 1.2

Multiply $4$ by $- 5$ .

$(4 x - 20) (x^{2} + x + 2)$

Step 2

Expand $(4 x - 20) (x^{2} + x + 2)$ by multiplying each term in the first expression by each term in the second expression.

$4 x \cdot x^{2} + 4 x \cdot x + 4 x \cdot 2 - 20 x^{2} - 20 x - 20 \cdot 2$

Step 3

Simplify terms.

Tap for more steps...

Step 3.1

Simplify each term.

Tap for more steps...

Step 3.1.1

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

Tap for more steps...

Step 3.1.1.1

Move $x^{2}$ .

$4 (x^{2} x) + 4 x \cdot x + 4 x \cdot 2 - 20 x^{2} - 20 x - 20 \cdot 2$

Step 3.1.1.2

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

Tap for more steps...

Step 3.1.1.2.1

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

$4 (x^{2} x^{1}) + 4 x \cdot x + 4 x \cdot 2 - 20 x^{2} - 20 x - 20 \cdot 2$

Step 3.1.1.2.2

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

$4 x^{2 + 1} + 4 x \cdot x + 4 x \cdot 2 - 20 x^{2} - 20 x - 20 \cdot 2$

Step 3.1.1.3

Add $2$ and $1$ .

$4 x^{3} + 4 x \cdot x + 4 x \cdot 2 - 20 x^{2} - 20 x - 20 \cdot 2$

Step 3.1.2

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

Tap for more steps...

Step 3.1.2.1

Move $x$ .

$4 x^{3} + 4 (x \cdot x) + 4 x \cdot 2 - 20 x^{2} - 20 x - 20 \cdot 2$

Step 3.1.2.2

Multiply $x$ by $x$ .

$4 x^{3} + 4 x^{2} + 4 x \cdot 2 - 20 x^{2} - 20 x - 20 \cdot 2$

Step 3.1.3

Multiply $2$ by $4$ .

$4 x^{3} + 4 x^{2} + 8 x - 20 x^{2} - 20 x - 20 \cdot 2$

Step 3.1.4

Multiply $- 20$ by $2$ .

$4 x^{3} + 4 x^{2} + 8 x - 20 x^{2} - 20 x - 40$

Step 3.2

Simplify by adding terms.

Tap for more steps...

Step 3.2.1

Subtract $20 x^{2}$ from $4 x^{2}$ .

$4 x^{3} - 16 x^{2} + 8 x - 20 x - 40$

Step 3.2.2

Subtract $20 x$ from $8 x$ .

$4 x^{3} - 16 x^{2} - 12 x - 40$