Simplify 5x^2(2x-3)

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

Step 1

Simplify by multiplying through.

Apply the distributive property.

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

Simplify the expression.

Rewrite using the commutative property of multiplication.

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

Multiply $- 3$ by $5$ .

$5 \cdot 2 x^{2} x - 15 x^{2}$

Step 2

Simplify each term.

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

Move $x$ .

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

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

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

$5 \cdot 2 (x^{1} x^{2}) - 15 x^{2}$

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

$5 \cdot 2 x^{1 + 2} - 15 x^{2}$

Add $1$ and $2$ .

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

Multiply $5$ by $2$ .

$10 x^{3} - 15 x^{2}$