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

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

Step 1

Apply the distributive property.

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

Step 2

Simplify.

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

Move $x^{2}$ .

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

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

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

$- 3 (x^{2} x^{1}) y^{2} (2 y^{3}) - 3 x y^{2} (7 x y^{2}) - 3 x y^{2} (- 5 x^{3} y^{2})$

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

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

Add $2$ and $1$ .

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

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

Move $x$ .

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

Multiply $x$ by $x$ .

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

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

Move $x^{3}$ .

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

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

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

$- 3 x^{3} y^{2} (2 y^{3}) - 3 x^{2} y^{2} (7 y^{2}) - 3 (x^{3} x^{1}) y^{2} (- 5 y^{2})$

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

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

Add $3$ and $1$ .

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

Step 3

Simplify each term.

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

Move $y^{3}$ .

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

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

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

Add $3$ and $2$ .

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

Multiply $2$ by $- 3$ .

$- 6 x^{3} y^{5} - 3 x^{2} y^{2} (7 y^{2}) - 3 x^{4} y^{2} (- 5 y^{2})$

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

Move $y^{2}$ .

$- 6 x^{3} y^{5} - 3 x^{2} (y^{2} y^{2}) \cdot 7 - 3 x^{4} y^{2} (- 5 y^{2})$

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

$- 6 x^{3} y^{5} - 3 x^{2} y^{2 + 2} \cdot 7 - 3 x^{4} y^{2} (- 5 y^{2})$

Add $2$ and $2$ .

$- 6 x^{3} y^{5} - 3 x^{2} y^{4} \cdot 7 - 3 x^{4} y^{2} (- 5 y^{2})$

Multiply $7$ by $- 3$ .

$- 6 x^{3} y^{5} - 21 x^{2} y^{4} - 3 x^{4} y^{2} (- 5 y^{2})$

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

Move $y^{2}$ .

$- 6 x^{3} y^{5} - 21 x^{2} y^{4} - 3 x^{4} (y^{2} y^{2}) \cdot - 5$

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

$- 6 x^{3} y^{5} - 21 x^{2} y^{4} - 3 x^{4} y^{2 + 2} \cdot - 5$

Add $2$ and $2$ .

$- 6 x^{3} y^{5} - 21 x^{2} y^{4} - 3 x^{4} y^{4} \cdot - 5$

Multiply $- 5$ by $- 3$ .

$- 6 x^{3} y^{5} - 21 x^{2} y^{4} + 15 x^{4} y^{4}$

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

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