Solve 4*(1/2x-y)^2

$$4 \cdot ( \frac { 1 } { 2 } x - y ) ^ { 2 }$$

Evaluate

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

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(\frac{1}{2}x-y\right)^{2}.

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

Use the distributive property to multiply 4 by \frac{1}{4}x^{2}-xy+y^{2}.

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

Expand

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

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(\frac{1}{2}x-y\right)^{2}.

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

Use the distributive property to multiply 4 by \frac{1}{4}x^{2}-xy+y^{2}.

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