Solve (-2x^{2})(-x^{2}y^5)-(3x^2y)^2*y^3

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

Evaluate

$$-7x^{4}y^{5}$$

Solution Steps

Multiply -2 and -1 to get 2.

$$2x^{2}x^{2}y^{5}-\left(3x^{2}y\right)^{2}y^{3}$$

To multiply powers of the same base, add their exponents. Add 2 and 2 to get 4.

$$2x^{4}y^{5}-\left(3x^{2}y\right)^{2}y^{3}$$

Expand \left(3x^{2}y\right)^{2}.

$$2x^{4}y^{5}-3^{2}\left(x^{2}\right)^{2}y^{2}y^{3}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

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

Calculate 3 to the power of 2 and get 9.

$$2x^{4}y^{5}-9x^{4}y^{2}y^{3}$$

To multiply powers of the same base, add their exponents. Add 2 and 3 to get 5.

$$2x^{4}y^{5}-9x^{4}y^{5}$$

Combine 2x^{4}y^{5} and -9x^{4}y^{5} to get -7x^{4}y^{5}.

$$-7x^{4}y^{5}$$

Expand

$$-7x^{4}y^{5}$$

Solution Steps

Multiply -2 and -1 to get 2.

$$2x^{2}x^{2}y^{5}-\left(3x^{2}y\right)^{2}y^{3}$$

To multiply powers of the same base, add their exponents. Add 2 and 2 to get 4.

$$2x^{4}y^{5}-\left(3x^{2}y\right)^{2}y^{3}$$

Expand \left(3x^{2}y\right)^{2}.

$$2x^{4}y^{5}-3^{2}\left(x^{2}\right)^{2}y^{2}y^{3}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

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

Calculate 3 to the power of 2 and get 9.

$$2x^{4}y^{5}-9x^{4}y^{2}y^{3}$$

To multiply powers of the same base, add their exponents. Add 2 and 3 to get 5.

$$2x^{4}y^{5}-9x^{4}y^{5}$$

Combine 2x^{4}y^{5} and -9x^{4}y^{5} to get -7x^{4}y^{5}.

$$-7x^{4}y^{5}$$