Solve 10(-2y)^2-(x-y)(x+y)-2y^2

$$10 ( - 2 y ) ^ { 2 } - ( x - y ) ( x + y ) - 2 y ^ { 2 }$$

Evaluate

$$39y^{2}-x^{2}$$

Solution Steps

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

$$10\left(-2\right)^{2}y^{2}-\left(x-y\right)\left(x+y\right)-2y^{2}$$

Calculate -2 to the power of 2 and get 4.

$$10\times 4y^{2}-\left(x-y\right)\left(x+y\right)-2y^{2}$$

Multiply 10 and 4 to get 40.

$$40y^{2}-\left(x-y\right)\left(x+y\right)-2y^{2}$$

Consider \left(x-y\right)\left(x+y\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$40y^{2}-\left(x^{2}-y^{2}\right)-2y^{2}$$

To find the opposite of x^{2}-y^{2}, find the opposite of each term.

$$40y^{2}-x^{2}+y^{2}-2y^{2}$$

Combine 40y^{2} and y^{2} to get 41y^{2}.

$$41y^{2}-x^{2}-2y^{2}$$

Combine 41y^{2} and -2y^{2} to get 39y^{2}.

$$39y^{2}-x^{2}$$

Expand

$$39y^{2}-x^{2}$$

Solution Steps

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

$$10\left(-2\right)^{2}y^{2}-\left(x-y\right)\left(x+y\right)-2y^{2}$$

Calculate -2 to the power of 2 and get 4.

$$10\times 4y^{2}-\left(x-y\right)\left(x+y\right)-2y^{2}$$

Multiply 10 and 4 to get 40.

$$40y^{2}-\left(x-y\right)\left(x+y\right)-2y^{2}$$

Consider \left(x-y\right)\left(x+y\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$40y^{2}-\left(x^{2}-y^{2}\right)-2y^{2}$$

To find the opposite of x^{2}-y^{2}, find the opposite of each term.

$$40y^{2}-x^{2}+y^{2}-2y^{2}$$

Combine 40y^{2} and y^{2} to get 41y^{2}.

$$41y^{2}-x^{2}-2y^{2}$$

Combine 41y^{2} and -2y^{2} to get 39y^{2}.

$$39y^{2}-x^{2}$$