Algebra Examples

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

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 $(4 x + 5) (x^{2} - x - 4)$ by multiplying each term in the first expression by each term in the second expression.

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

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 $x^{2}$ .

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

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 $1$ .

$4 (x^{2} x^{1}) + 4 x (- x) + 4 x \cdot - 4 + 5 x^{2} + 5 (- x) + 5 \cdot - 4$

Step 3.1.1.2.2

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

$4 x^{2 + 1} + 4 x (- x) + 4 x \cdot - 4 + 5 x^{2} + 5 (- x) + 5 \cdot - 4$

Step 3.1.1.3

Add $2$ and $1$ .

$4 x^{3} + 4 x (- x) + 4 x \cdot - 4 + 5 x^{2} + 5 (- x) + 5 \cdot - 4$

Step 3.1.2

Rewrite using the commutative property of multiplication.

$4 x^{3} + 4 \cdot - 1 x \cdot x + 4 x \cdot - 4 + 5 x^{2} + 5 (- x) + 5 \cdot - 4$

Step 3.1.3

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

Tap for more steps...

Step 3.1.3.1

Move $x$ .

$4 x^{3} + 4 \cdot - 1 (x \cdot x) + 4 x \cdot - 4 + 5 x^{2} + 5 (- x) + 5 \cdot - 4$

Step 3.1.3.2

Multiply $x$ by $x$ .

$4 x^{3} + 4 \cdot - 1 x^{2} + 4 x \cdot - 4 + 5 x^{2} + 5 (- x) + 5 \cdot - 4$

Step 3.1.4

Multiply $4$ by $- 1$ .

$4 x^{3} - 4 x^{2} + 4 x \cdot - 4 + 5 x^{2} + 5 (- x) + 5 \cdot - 4$

Step 3.1.5

Multiply $- 4$ by $4$ .

$4 x^{3} - 4 x^{2} - 16 x + 5 x^{2} + 5 (- x) + 5 \cdot - 4$

Step 3.1.6

Multiply $- 1$ by $5$ .

$4 x^{3} - 4 x^{2} - 16 x + 5 x^{2} - 5 x + 5 \cdot - 4$

Step 3.1.7

Multiply $5$ by $- 4$ .

$4 x^{3} - 4 x^{2} - 16 x + 5 x^{2} - 5 x - 20$

Step 3.2

Simplify by adding terms.

Tap for more steps...

Step 3.2.1

Add $- 4 x^{2}$ and $5 x^{2}$ .

$4 x^{3} + x^{2} - 16 x - 5 x - 20$

Step 3.2.2

Subtract $5 x$ from $- 16 x$ .

$4 x^{3} + x^{2} - 21 x - 20$