Simplify 2x(y^2+3xy+4x+3)

$2 x (y^{2} + 3 x y + 4 x + 3)$

Step 1

Apply the distributive property.

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

Step 2

Simplify.

Multiply $x$ by $x$ by adding the exponents.

Move $x$ .

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

Multiply $x$ by $x$ .

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

Rewrite using the commutative property of multiplication.

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

Multiply $3$ by $2$ .

$2 x y^{2} + 2 x^{2} (3 y) + 2 \cdot 4 x \cdot x + 6 x$

Step 3

Simplify each term.

Rewrite using the commutative property of multiplication.

$2 x y^{2} + 2 \cdot 3 x^{2} y + 2 \cdot 4 x \cdot x + 6 x$

Multiply $2$ by $3$ .

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

Multiply $x$ by $x$ by adding the exponents.

Move $x$ .

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

Multiply $x$ by $x$ .

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

Multiply $2$ by $4$ .

$2 x y^{2} + 6 x^{2} y + 8 x^{2} + 6 x$

Step 4

Reorder $2 x y^{2}$ and $6 x^{2} y$ .

$6 x^{2} y + 2 x y^{2} + 8 x^{2} + 6 x$