Simplify 2x(x+5)-x^2(3-x)

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

Step 1

Simplify each term.

Apply the distributive property.

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

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

Move $x$ .

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

Multiply $x$ by $x$ .

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

Multiply $5$ by $2$ .

$2 x^{2} + 10 x - x^{2} (3 - x)$

Apply the distributive property.

$2 x^{2} + 10 x - x^{2} \cdot 3 - x^{2} (- x)$

Multiply $3$ by $- 1$ .

$2 x^{2} + 10 x - 3 x^{2} - x^{2} (- x)$

Rewrite using the commutative property of multiplication.

$2 x^{2} + 10 x - 3 x^{2} - 1 \cdot - 1 x^{2} x$

Simplify each term.

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

Move $x$ .

$2 x^{2} + 10 x - 3 x^{2} - 1 \cdot - 1 (x \cdot x^{2})$

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

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

$2 x^{2} + 10 x - 3 x^{2} - 1 \cdot - 1 (x^{1} x^{2})$

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

$2 x^{2} + 10 x - 3 x^{2} - 1 \cdot - 1 x^{1 + 2}$

Add $1$ and $2$ .

$2 x^{2} + 10 x - 3 x^{2} - 1 \cdot - 1 x^{3}$

Multiply $- 1$ by $- 1$ .

$2 x^{2} + 10 x - 3 x^{2} + 1 x^{3}$

Multiply $x^{3}$ by $1$ .

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

Step 2

Simplify by adding terms.

Subtract $3 x^{2}$ from $2 x^{2}$ .

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

Simplify the expression.

Move $10 x$ .

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

Reorder $- x^{2}$ and $x^{3}$ .

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