Write in Standard Form 2x(3x^3+5y)

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

Step 1

To write a polynomial in standard form, simplify and then arrange the terms in descending order.

$a x^{2} + b x + c$

Step 2

Simplify by multiplying through.

Apply the distributive property.

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

Reorder.

Rewrite using the commutative property of multiplication.

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

Rewrite using the commutative property of multiplication.

$2 \cdot 3 x \cdot x^{3} + 2 \cdot 5 x y$

Step 3

Simplify each term.

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

Move $x^{3}$ .

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

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

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

$2 \cdot 3 (x^{3} x^{1}) + 2 \cdot 5 x y$

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

$2 \cdot 3 x^{3 + 1} + 2 \cdot 5 x y$

Add $3$ and $1$ .

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

Multiply $2$ by $3$ .

$6 x^{4} + 2 \cdot 5 x y$

Multiply $2$ by $5$ .

$6 x^{4} + 10 x y$