Simplify 2x^2(x^3-5)-x(x^4-3x)

$2 x^{2} (x^{3} - 5) - x (x^{4} - 3 x)$

Step 1

Simplify each term.

Apply the distributive property.

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

Multiply $x^{2}$ by $x^{3}$ by adding the exponents.

Move $x^{3}$ .

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

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

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

Add $3$ and $2$ .

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

Multiply $- 5$ by $2$ .

$2 x^{5} - 10 x^{2} - x (x^{4} - 3 x)$

Apply the distributive property.

$2 x^{5} - 10 x^{2} - x \cdot x^{4} - x (- 3 x)$

Multiply $x$ by $x^{4}$ by adding the exponents.

Move $x^{4}$ .

$2 x^{5} - 10 x^{2} - (x^{4} x) - x (- 3 x)$

Multiply $x^{4}$ by $x$ .

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

$2 x^{5} - 10 x^{2} - (x^{4} x^{1}) - x (- 3 x)$

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

$2 x^{5} - 10 x^{2} - x^{4 + 1} - x (- 3 x)$

Add $4$ and $1$ .

$2 x^{5} - 10 x^{2} - x^{5} - x (- 3 x)$

Rewrite using the commutative property of multiplication.

$2 x^{5} - 10 x^{2} - x^{5} - 1 \cdot - 3 x \cdot x$

Simplify each term.

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

Move $x$ .

$2 x^{5} - 10 x^{2} - x^{5} - 1 \cdot - 3 (x \cdot x)$

Multiply $x$ by $x$ .

$2 x^{5} - 10 x^{2} - x^{5} - 1 \cdot - 3 x^{2}$

Multiply $- 1$ by $- 3$ .

$2 x^{5} - 10 x^{2} - x^{5} + 3 x^{2}$

Step 2

Simplify by adding terms.

Subtract $x^{5}$ from $2 x^{5}$ .

$x^{5} - 10 x^{2} + 3 x^{2}$

Add $- 10 x^{2}$ and $3 x^{2}$ .

$x^{5} - 7 x^{2}$