Find the Product (4x^2y+3xy-x^2)(-x^3y^2)

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

Apply the distributive property.

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

Simplify.

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

Move $x^{3}$ .

$4 (x^{3} x^{2}) y (- 1 y^{2}) + 3 x y (- x^{3} y^{2}) - x^{2} (- x^{3} y^{2})$

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

$4 x^{3 + 2} y (- 1 y^{2}) + 3 x y (- x^{3} y^{2}) - x^{2} (- x^{3} y^{2})$

Add $3$ and $2$ .

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

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

Move $x^{3}$ .

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

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

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

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

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

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

Add $3$ and $1$ .

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

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

Move $x^{3}$ .

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

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

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

Add $3$ and $2$ .

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

Simplify each term.

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

Move $y^{2}$ .

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

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

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

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

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

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

Add $2$ and $1$ .

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

Multiply $- 1$ by $4$ .

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

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

Move $y^{2}$ .

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

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

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

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

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

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

Add $2$ and $1$ .

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

Multiply $- 1$ by $3$ .

$- 4 x^{5} y^{3} - 3 x^{4} y^{3} - x^{5} (- 1 y^{2})$

Rewrite using the commutative property of multiplication.

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

Multiply $- 1$ by $- 1$ .

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

Multiply $x^{5}$ by $1$ .

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

Find the Product (4x^2y+3xy-x^2)(-x^3y^2)

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