Simplify 7xy(3x^2+4y+2)

$7 x y (3 x^{2} + 4 y + 2)$

Apply the distributive property.

$7 x y (3 x^{2}) + 7 x y (4 y) + 7 x y \cdot 2$

Simplify.

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

Move $x^{2}$ .

$7 (x^{2} x) y \cdot 3 + 7 x y (4 y) + 7 x y \cdot 2$

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

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

$7 (x^{2} x^{1}) y \cdot 3 + 7 x y (4 y) + 7 x y \cdot 2$

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

$7 x^{2 + 1} y \cdot 3 + 7 x y (4 y) + 7 x y \cdot 2$

Add $2$ and $1$ .

$7 x^{3} y \cdot 3 + 7 x y (4 y) + 7 x y \cdot 2$

Multiply $y$ by $y$ by adding the exponents.

Move $y$ .

$7 x^{3} y \cdot 3 + 7 x (y \cdot y) \cdot 4 + 7 x y \cdot 2$

Multiply $y$ by $y$ .

$7 x^{3} y \cdot 3 + 7 x y^{2} \cdot 4 + 7 x y \cdot 2$

Multiply $2$ by $7$ .

$7 x^{3} y \cdot 3 + 7 x y^{2} \cdot 4 + 14 x y$

Simplify each term.

Multiply $3$ by $7$ .

$21 x^{3} y + 7 x y^{2} \cdot 4 + 14 x y$

Multiply $4$ by $7$ .

$21 x^{3} y + 28 x y^{2} + 14 x y$