Simplify 5x^2(8x^5-3x^3+4x)

$5 x^{2} (8 x^{5} - 3 x^{3} + 4 x)$

Step 1

Apply the distributive property.

$5 x^{2} (8 x^{5}) + 5 x^{2} (- 3 x^{3}) + 5 x^{2} (4 x)$

Step 2

Simplify.

Rewrite using the commutative property of multiplication.

$5 \cdot 8 x^{2} x^{5} + 5 x^{2} (- 3 x^{3}) + 5 x^{2} (4 x)$

Rewrite using the commutative property of multiplication.

$5 \cdot 8 x^{2} x^{5} + 5 \cdot - 3 x^{2} x^{3} + 5 x^{2} (4 x)$

Rewrite using the commutative property of multiplication.

$5 \cdot 8 x^{2} x^{5} + 5 \cdot - 3 x^{2} x^{3} + 5 \cdot 4 x^{2} x$

Step 3

Simplify each term.

Multiply $x^{2}$ by $x^{5}$ by adding the exponents.

Move $x^{5}$ .

$5 \cdot 8 (x^{5} x^{2}) + 5 \cdot - 3 x^{2} x^{3} + 5 \cdot 4 x^{2} x$

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

$5 \cdot 8 x^{5 + 2} + 5 \cdot - 3 x^{2} x^{3} + 5 \cdot 4 x^{2} x$

Add $5$ and $2$ .

$5 \cdot 8 x^{7} + 5 \cdot - 3 x^{2} x^{3} + 5 \cdot 4 x^{2} x$

Multiply $5$ by $8$ .

$40 x^{7} + 5 \cdot - 3 x^{2} x^{3} + 5 \cdot 4 x^{2} x$

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

Move $x^{3}$ .

$40 x^{7} + 5 \cdot - 3 (x^{3} x^{2}) + 5 \cdot 4 x^{2} x$

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

$40 x^{7} + 5 \cdot - 3 x^{3 + 2} + 5 \cdot 4 x^{2} x$

Add $3$ and $2$ .

$40 x^{7} + 5 \cdot - 3 x^{5} + 5 \cdot 4 x^{2} x$

Multiply $5$ by $- 3$ .

$40 x^{7} - 15 x^{5} + 5 \cdot 4 x^{2} x$

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

Move $x$ .

$40 x^{7} - 15 x^{5} + 5 \cdot 4 (x \cdot x^{2})$

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

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

$40 x^{7} - 15 x^{5} + 5 \cdot 4 (x^{1} x^{2})$

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

$40 x^{7} - 15 x^{5} + 5 \cdot 4 x^{1 + 2}$

Add $1$ and $2$ .

$40 x^{7} - 15 x^{5} + 5 \cdot 4 x^{3}$

Multiply $5$ by $4$ .

$40 x^{7} - 15 x^{5} + 20 x^{3}$