Solve 3/8(4-5/3t)^2

$$\frac { 3 } { 8 } ( 4 - \frac { 5 } { 3 } t ) ^ { 2 }$$

Evaluate

$$\frac{\left(12-5t\right)^{2}}{24}$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(4-\frac{5}{3}t\right)^{2}.

$$\frac{3}{8}\left(16-\frac{40}{3}t+\frac{25}{9}t^{2}\right)$$

Use the distributive property to multiply \frac{3}{8} by 16-\frac{40}{3}t+\frac{25}{9}t^{2}.

$$6-5t+\frac{25}{24}t^{2}$$

Expand

$$\frac{25t^{2}}{24}-5t+6$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(4-\frac{5}{3}t\right)^{2}.

$$\frac{3}{8}\left(16-\frac{40}{3}t+\frac{25}{9}t^{2}\right)$$

Use the distributive property to multiply \frac{3}{8} by 16-\frac{40}{3}t+\frac{25}{9}t^{2}.

$$6-5t+\frac{25}{24}t^{2}$$