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2\left(x^{2}-\frac{2}{3}x+\frac{1}{9}\right)+1-\frac{1}{9}
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-\frac{1}{3}\right)^{2}.
2x^{2}-\frac{4}{3}x+\frac{2}{9}+1-\frac{1}{9}
Use the distributive property to multiply 2 by x^{2}-\frac{2}{3}x+\frac{1}{9}.
2x^{2}-\frac{4}{3}x+\frac{11}{9}-\frac{1}{9}
Add \frac{2}{9} and 1 to get \frac{11}{9}.
2x^{2}-\frac{4}{3}x+\frac{10}{9}
Subtract \frac{1}{9} from \frac{11}{9} to get \frac{10}{9}.
2\left(x^{2}-\frac{2}{3}x+\frac{1}{9}\right)+1-\frac{1}{9}
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-\frac{1}{3}\right)^{2}.
2x^{2}-\frac{4}{3}x+\frac{2}{9}+1-\frac{1}{9}
Use the distributive property to multiply 2 by x^{2}-\frac{2}{3}x+\frac{1}{9}.
2x^{2}-\frac{4}{3}x+\frac{11}{9}-\frac{1}{9}
Add \frac{2}{9} and 1 to get \frac{11}{9}.
2x^{2}-\frac{4}{3}x+\frac{10}{9}
Subtract \frac{1}{9} from \frac{11}{9} to get \frac{10}{9}.