Precalculus Examples

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

Step 1

Simplify each term.

Tap for more steps...

Step 1.1

Apply the distributive property.

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

Step 1.2

Rewrite using the commutative property of multiplication.

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

Step 1.3

Multiply $- 5$ by $3$ .

$2 x + 3 \cdot 4 x^{2} x - 15 x^{2}$

Step 1.4

Simplify each term.

Tap for more steps...

Step 1.4.1

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

Tap for more steps...

Step 1.4.1.1

Move $x$ .

$2 x + 3 \cdot 4 (x \cdot x^{2}) - 15 x^{2}$

Step 1.4.1.2

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

Tap for more steps...

Step 1.4.1.2.1

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

$2 x + 3 \cdot 4 (x^{1} x^{2}) - 15 x^{2}$

Step 1.4.1.2.2

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

$2 x + 3 \cdot 4 x^{1 + 2} - 15 x^{2}$

Step 1.4.1.3

Add $1$ and $2$ .

$2 x + 3 \cdot 4 x^{3} - 15 x^{2}$

Step 1.4.2

Multiply $3$ by $4$ .

$2 x + 12 x^{3} - 15 x^{2}$

Step 2

Move $2 x$ .

$12 x^{3} - 15 x^{2} + 2 x$