Simplify 7x^3y(x^2y-3x+2)+5x^4y

$7 x^{3} y (x^{2} y - 3 x + 2) + 5 x^{4} y$

Simplify each term.

Apply the distributive property.

$7 x^{3} y (x^{2} y) + 7 x^{3} y (- 3 x) + 7 x^{3} y \cdot 2 + 5 x^{4} y$

Simplify.

Multiply $x^{3}$ by $x^{2}$ by adding the exponents.

Move $x^{2}$ .

$7 (x^{2} x^{3}) y \cdot y + 7 x^{3} y (- 3 x) + 7 x^{3} y \cdot 2 + 5 x^{4} y$

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

$7 x^{2 + 3} y \cdot y + 7 x^{3} y (- 3 x) + 7 x^{3} y \cdot 2 + 5 x^{4} y$

Add $2$ and $3$ .

$7 x^{5} y \cdot y + 7 x^{3} y (- 3 x) + 7 x^{3} y \cdot 2 + 5 x^{4} y$

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

Move $x$ .

$7 x^{5} y \cdot y + 7 (x \cdot x^{3}) y \cdot - 3 + 7 x^{3} y \cdot 2 + 5 x^{4} y$

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

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

$7 x^{5} y \cdot y + 7 (x^{1} x^{3}) y \cdot - 3 + 7 x^{3} y \cdot 2 + 5 x^{4} y$

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

$7 x^{5} y \cdot y + 7 x^{1 + 3} y \cdot - 3 + 7 x^{3} y \cdot 2 + 5 x^{4} y$

Add $1$ and $3$ .

$7 x^{5} y \cdot y + 7 x^{4} y \cdot - 3 + 7 x^{3} y \cdot 2 + 5 x^{4} y$

Multiply $2$ by $7$ .

$7 x^{5} y \cdot y + 7 x^{4} y \cdot - 3 + 14 x^{3} y + 5 x^{4} y$

Simplify each term.

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

Move $y$ .

$7 x^{5} (y \cdot y) + 7 x^{4} y \cdot - 3 + 14 x^{3} y + 5 x^{4} y$

Multiply $y$ by $y$ .

$7 x^{5} y^{2} + 7 x^{4} y \cdot - 3 + 14 x^{3} y + 5 x^{4} y$

Multiply $- 3$ by $7$ .

$7 x^{5} y^{2} - 21 x^{4} y + 14 x^{3} y + 5 x^{4} y$

Add $- 21 x^{4} y$ and $5 x^{4} y$ .

$7 x^{5} y^{2} - 16 x^{4} y + 14 x^{3} y$