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

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

Evaluate

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

Solution Steps

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

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

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

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

Calculate 1 to the power of 2 and get 1.

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

Expand

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

Solution Steps

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

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

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

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

Calculate 1 to the power of 2 and get 1.

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