Solve 2y(x-2y)+(x+1)(x-1)

$$2 y ( x - 2 y ) + ( x + 1 ) ( x - 1 )$$

Evaluate

$$2y\left(x-2y\right)+x^{2}-1$$

Solution Steps

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

$$2yx-4y^{2}+\left(x+1\right)\left(x-1\right)$$

Consider \left(x+1\right)\left(x-1\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$2yx-4y^{2}+x^{2}-1^{2}$$

Calculate 1 to the power of 2 and get 1.

$$2yx-4y^{2}+x^{2}-1$$

Expand

$$x^{2}+2xy-4y^{2}-1$$

Solution Steps

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

$$2yx-4y^{2}+\left(x+1\right)\left(x-1\right)$$

Consider \left(x+1\right)\left(x-1\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$2yx-4y^{2}+x^{2}-1^{2}$$

Calculate 1 to the power of 2 and get 1.

$$2yx-4y^{2}+x^{2}-1$$