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

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

Evaluate

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

Solution Steps

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

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

Consider \left(1-y\right)\left(1+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}.

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

Calculate 1 to the power of 2 and get 1.

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

Expand

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

Solution Steps

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

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

Consider \left(1-y\right)\left(1+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}.

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

Calculate 1 to the power of 2 and get 1.

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