$$(0.5a+0.2b)(0.5a+0.2b$$
$\left(\frac{a}{2}+\frac{b}{5}\right)^{2}$
$$\left(0.5a+0.2b\right)^{2}$$
$$0.25a^{2}+0.2ab+0.04b^{2}$$
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$\frac{ab}{5}+\frac{a^{2}}{4}+\frac{b^{2}}{25}$