Solve (2m)(m-2y)-(2m-y)^2

$$( 2 m ) ( m - 2 y ) - ( 2 m - y ) ^ { 2 }$$

Evaluate

$$-y^{2}-2m^{2}$$

Solution Steps

Use the distributive property to multiply 2m by m-2y.

$$2m^{2}-4my-\left(2m-y\right)^{2}$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(2m-y\right)^{2}.

$$2m^{2}-4my-\left(4m^{2}-4my+y^{2}\right)$$

To find the opposite of 4m^{2}-4my+y^{2}, find the opposite of each term.

$$2m^{2}-4my-4m^{2}+4my-y^{2}$$

Combine 2m^{2} and -4m^{2} to get -2m^{2}.

$$-2m^{2}-4my+4my-y^{2}$$

Combine -4my and 4my to get 0.

$$-2m^{2}-y^{2}$$

Expand

$$-y^{2}-2m^{2}$$

Solution Steps

Use the distributive property to multiply 2m by m-2y.

$$2m^{2}-4my-\left(2m-y\right)^{2}$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(2m-y\right)^{2}.

$$2m^{2}-4my-\left(4m^{2}-4my+y^{2}\right)$$

To find the opposite of 4m^{2}-4my+y^{2}, find the opposite of each term.

$$2m^{2}-4my-4m^{2}+4my-y^{2}$$

Combine 2m^{2} and -4m^{2} to get -2m^{2}.

$$-2m^{2}-4my+4my-y^{2}$$

Combine -4my and 4my to get 0.

$$-2m^{2}-y^{2}$$