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

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

Step 1

Expand $(3 x - 2) (2 x^{2} + 5)$ using the FOIL Method.

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Step 2

Simplify each term.

Rewrite using the commutative property of multiplication.

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

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

Move $x^{2}$ .

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

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

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

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

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

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

Add $2$ and $1$ .

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

Multiply $3$ by $2$ .

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

Multiply $5$ by $3$ .

$6 x^{3} + 15 x - 2 (2 x^{2}) - 2 \cdot 5$

Multiply $2$ by $- 2$ .

$6 x^{3} + 15 x - 4 x^{2} - 2 \cdot 5$

Multiply $- 2$ by $5$ .

$6 x^{3} + 15 x - 4 x^{2} - 10$