Solve 2/3(1/2l-2)^2

$$\frac { 2 } { 3 } ( \frac { 1 } { 2 } l - 2 ) ^ { 2 }$$

Evaluate

$$\frac{\left(l-4\right)^{2}}{6}$$

Solution Steps

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

$$\frac{2}{3}\left(\frac{1}{4}l^{2}-2l+4\right)$$

Use the distributive property to multiply \frac{2}{3} by \frac{1}{4}l^{2}-2l+4.

$$\frac{1}{6}l^{2}-\frac{4}{3}l+\frac{8}{3}$$

Expand

$$\frac{l^{2}}{6}-\frac{4l}{3}+\frac{8}{3}$$

Solution Steps

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

$$\frac{2}{3}\left(\frac{1}{4}l^{2}-2l+4\right)$$

Use the distributive property to multiply \frac{2}{3} by \frac{1}{4}l^{2}-2l+4.

$$\frac{1}{6}l^{2}-\frac{4}{3}l+\frac{8}{3}$$