Solve 3(x-2/3)^2+5/2

$$3 ( x - \frac { 2 } { 3 } ) ^ { 2 } + \frac { 5 } { 2 }$$

Evaluate

$$\frac{\left(3x-2\right)^{2}}{3}+\frac{5}{2}$$

Solution Steps

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

$$3\left(x^{2}-\frac{4}{3}x+\frac{4}{9}\right)+\frac{5}{2}$$

Use the distributive property to multiply 3 by x^{2}-\frac{4}{3}x+\frac{4}{9}.

$$3x^{2}-4x+\frac{4}{3}+\frac{5}{2}$$

Add \frac{4}{3} and \frac{5}{2} to get \frac{23}{6}.

$$3x^{2}-4x+\frac{23}{6}$$

Expand

$$3x^{2}-4x+\frac{23}{6}$$

Solution Steps

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

$$3\left(x^{2}-\frac{4}{3}x+\frac{4}{9}\right)+\frac{5}{2}$$

Use the distributive property to multiply 3 by x^{2}-\frac{4}{3}x+\frac{4}{9}.

$$3x^{2}-4x+\frac{4}{3}+\frac{5}{2}$$

Add \frac{4}{3} and \frac{5}{2} to get \frac{23}{6}.

$$3x^{2}-4x+\frac{23}{6}$$