Find the Product (2x^2+5x)(3x-2)

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

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

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

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

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

Move $x$ .

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

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

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

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

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

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

Add $1$ and $2$ .

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

Multiply $2$ by $3$ .

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

Multiply $- 2$ by $2$ .

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

Rewrite using the commutative property of multiplication.

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

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

Move $x$ .

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

Multiply $x$ by $x$ .

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

Multiply $5$ by $3$ .

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

Multiply $- 2$ by $5$ .

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

Add $- 4 x^{2}$ and $15 x^{2}$ .

$6 x^{3} + 11 x^{2} - 10 x$