Simplify 2a^3(5a^2-7a)+(3a^4-a^5)

$2 a^{3} (5 a^{2} - 7 a) + (3 a^{4} - a^{5})$

Remove parentheses.

$2 a^{3} (5 a^{2} - 7 a) + 3 a^{4} - a^{5}$

Simplify each term.

Apply the distributive property.

$2 a^{3} (5 a^{2}) + 2 a^{3} (- 7 a) + 3 a^{4} - a^{5}$

Rewrite using the commutative property of multiplication.

$2 \cdot 5 a^{3} a^{2} + 2 a^{3} (- 7 a) + 3 a^{4} - a^{5}$

Rewrite using the commutative property of multiplication.

$2 \cdot 5 a^{3} a^{2} + 2 \cdot - 7 a^{3} a + 3 a^{4} - a^{5}$

Simplify each term.

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

Move $a^{2}$ .

$2 \cdot 5 (a^{2} a^{3}) + 2 \cdot - 7 a^{3} a + 3 a^{4} - a^{5}$

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

$2 \cdot 5 a^{2 + 3} + 2 \cdot - 7 a^{3} a + 3 a^{4} - a^{5}$

Add $2$ and $3$ .

$2 \cdot 5 a^{5} + 2 \cdot - 7 a^{3} a + 3 a^{4} - a^{5}$

Multiply $2$ by $5$ .

$10 a^{5} + 2 \cdot - 7 a^{3} a + 3 a^{4} - a^{5}$

Multiply $a^{3}$ by $a$ by adding the exponents.

Move $a$ .

$10 a^{5} + 2 \cdot - 7 (a \cdot a^{3}) + 3 a^{4} - a^{5}$

Multiply $a$ by $a^{3}$ .

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

$10 a^{5} + 2 \cdot - 7 (a^{1} a^{3}) + 3 a^{4} - a^{5}$

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

$10 a^{5} + 2 \cdot - 7 a^{1 + 3} + 3 a^{4} - a^{5}$

Add $1$ and $3$ .

$10 a^{5} + 2 \cdot - 7 a^{4} + 3 a^{4} - a^{5}$

Multiply $2$ by $- 7$ .

$10 a^{5} - 14 a^{4} + 3 a^{4} - a^{5}$

Simplify by adding terms.

Subtract $a^{5}$ from $10 a^{5}$ .

$9 a^{5} - 14 a^{4} + 3 a^{4}$

Add $- 14 a^{4}$ and $3 a^{4}$ .

$9 a^{5} - 11 a^{4}$