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[tex]\large\boxed{\begin{array}{l}\sf a^2+b^2=(a+b)^2-2ab\\\sf a^2+b^2=\bigg(\dfrac{1}{2}+\dfrac{1}{2}\bigg)^2-2\cdot\dfrac{1}{2}\cdot\dfrac{1}{2}\\\sf a^2+b^2=1^2-\dfrac{2}{4}\\\sf a^2+b^2=\dfrac{4-2}{4}\\\sf a^2+b^2=\dfrac{2\div2}{4\div2}\\\sf a^2+b^2=\dfrac{1}{2}\end{array}}[/tex]
