Expand the Trigonometric Expression 3x(x^2-5x+6)

$3 x (x^{2} - 5 x + 6)$

Step 1

Apply the distributive property.

$3 x \cdot x^{2} + 3 x (- 5 x) + 3 x \cdot 6$

Step 2

Simplify.

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

Move $x^{2}$ .

$3 (x^{2} x) + 3 x (- 5 x) + 3 x \cdot 6$

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

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

$3 (x^{2} x^{1}) + 3 x (- 5 x) + 3 x \cdot 6$

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

$3 x^{2 + 1} + 3 x (- 5 x) + 3 x \cdot 6$

Add $2$ and $1$ .

$3 x^{3} + 3 x (- 5 x) + 3 x \cdot 6$

Rewrite using the commutative property of multiplication.

$3 x^{3} + 3 \cdot - 5 x \cdot x + 3 x \cdot 6$

Multiply $6$ by $3$ .

$3 x^{3} + 3 \cdot - 5 x \cdot x + 18 x$

Step 3

Simplify each term.

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

Move $x$ .

$3 x^{3} + 3 \cdot - 5 (x \cdot x) + 18 x$

Multiply $x$ by $x$ .

$3 x^{3} + 3 \cdot - 5 x^{2} + 18 x$

Multiply $3$ by $- 5$ .

$3 x^{3} - 15 x^{2} + 18 x$