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

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

Step 1

Apply the distributive property.

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

Step 2

Simplify.

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

Move $x$ .

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

Multiply $x$ by $x$ .

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

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

Move $x$ .

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

Multiply $x$ by $x$ .

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

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

Move $y^{2}$ .

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

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

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

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

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

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

Add $2$ and $1$ .

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

Step 3

Simplify each term.

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

Move $y^{3}$ .

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

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

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

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

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

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

Add $3$ and $1$ .

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

Multiply $3$ by $- 2$ .

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

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

Move $y$ .

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

Multiply $y$ by $y$ .

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

Multiply $- 5$ by $- 2$ .

$- 6 x^{2} y^{4} + 10 x^{2} y^{2} - 2 x y^{3} \cdot 7$

Multiply $7$ by $- 2$ .

$- 6 x^{2} y^{4} + 10 x^{2} y^{2} - 14 x y^{3}$

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

Related Questions

Support LCMGCF.com by disabling your adblocker.