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

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

Simplify each term.

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

Move $x^{2}$ .

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

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

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

Add $2$ and $2$ .

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

Multiply $- 3$ by $5$ .

$- 15 x^{4} y + (4 x) (4 x^{3} y)$

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

Move $x^{3}$ .

$- 15 x^{4} y + 4 (x^{3} x) (4 y)$

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

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

$- 15 x^{4} y + 4 (x^{3} x^{1}) (4 y)$

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

$- 15 x^{4} y + 4 x^{3 + 1} (4 y)$

Add $3$ and $1$ .

$- 15 x^{4} y + 4 x^{4} (4 y)$

Rewrite using the commutative property of multiplication.

$- 15 x^{4} y + 4 \cdot 4 x^{4} y$

Multiply $4$ by $4$ .

$- 15 x^{4} y + 16 x^{4} y$

Simplify by adding terms.

Add $- 15 x^{4} y$ and $16 x^{4} y$ .

$1 x^{4} y$

Multiply $x^{4}$ by $1$ .

$x^{4} y$