Simplify 5x^2(2x^2+13x-5)

$5 x^{2} (2 x^{2} + 13 x - 5)$

Step 1

Apply the distributive property.

$5 x^{2} (2 x^{2}) + 5 x^{2} (13 x) + 5 x^{2} \cdot - 5$

Step 2

Simplify.

Rewrite using the commutative property of multiplication.

$5 \cdot 2 x^{2} x^{2} + 5 x^{2} (13 x) + 5 x^{2} \cdot - 5$

Rewrite using the commutative property of multiplication.

$5 \cdot 2 x^{2} x^{2} + 5 \cdot 13 x^{2} x + 5 x^{2} \cdot - 5$

Multiply $- 5$ by $5$ .

$5 \cdot 2 x^{2} x^{2} + 5 \cdot 13 x^{2} x - 25 x^{2}$

Step 3

Simplify each term.

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

Move $x^{2}$ .

$5 \cdot 2 (x^{2} x^{2}) + 5 \cdot 13 x^{2} x - 25 x^{2}$

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

$5 \cdot 2 x^{2 + 2} + 5 \cdot 13 x^{2} x - 25 x^{2}$

Add $2$ and $2$ .

$5 \cdot 2 x^{4} + 5 \cdot 13 x^{2} x - 25 x^{2}$

Multiply $5$ by $2$ .

$10 x^{4} + 5 \cdot 13 x^{2} x - 25 x^{2}$

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

Move $x$ .

$10 x^{4} + 5 \cdot 13 (x \cdot x^{2}) - 25 x^{2}$

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

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

$10 x^{4} + 5 \cdot 13 (x^{1} x^{2}) - 25 x^{2}$

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

$10 x^{4} + 5 \cdot 13 x^{1 + 2} - 25 x^{2}$

Add $1$ and $2$ .

$10 x^{4} + 5 \cdot 13 x^{3} - 25 x^{2}$

Multiply $5$ by $13$ .

$10 x^{4} + 65 x^{3} - 25 x^{2}$