Solve 3(1/3b-a)^2

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

Evaluate

$$\frac{\left(b-3a\right)^{2}}{3}$$

Solution Steps

Use binomial theorem \left(p-q\right)^{2}=p^{2}-2pq+q^{2} to expand \left(\frac{1}{3}b-a\right)^{2}.

$$3\left(\frac{1}{9}b^{2}-\frac{2}{3}ba+a^{2}\right)$$

Use the distributive property to multiply 3 by \frac{1}{9}b^{2}-\frac{2}{3}ba+a^{2}.

$$\frac{1}{3}b^{2}-2ba+3a^{2}$$

Expand

$$-2ab+\frac{b^{2}}{3}+3a^{2}$$

Solution Steps

Use binomial theorem \left(p-q\right)^{2}=p^{2}-2pq+q^{2} to expand \left(\frac{1}{3}b-a\right)^{2}.

$$3\left(\frac{1}{9}b^{2}-\frac{2}{3}ba+a^{2}\right)$$

Use the distributive property to multiply 3 by \frac{1}{9}b^{2}-\frac{2}{3}ba+a^{2}.

$$\frac{1}{3}b^{2}-2ba+3a^{2}$$