Write in Standard Form 4x(2x^2+y)

$4 x (2 x^{2} + y)$

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.

$4 x (2 x^{2}) + 4 x y$

Rewrite using the commutative property of multiplication.

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

Step 3

Simplify each term.

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

Move $x^{2}$ .

$4 \cdot 2 (x^{2} x) + 4 x y$

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

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

$4 \cdot 2 (x^{2} x^{1}) + 4 x y$

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

$4 \cdot 2 x^{2 + 1} + 4 x y$

Add $2$ and $1$ .

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

Multiply $4$ by $2$ .

$8 x^{3} + 4 x y$