$$(100+2)^{2}=100^{2}\{2(100+2)+2(100+2)+2^{2}\}$$
$\text{false}$
$$102^{2}=100^{2}\left(2\left(100+2\right)+2\left(100+2\right)+2^{2}\right)$$
$$10404=100^{2}\left(2\left(100+2\right)+2\left(100+2\right)+2^{2}\right)$$
$$10404=10000\left(2\left(100+2\right)+2\left(100+2\right)+2^{2}\right)$$
$$10404=10000\left(2\times 102+2\left(100+2\right)+2^{2}\right)$$
$$10404=10000\left(204+2\left(100+2\right)+2^{2}\right)$$
$$10404=10000\left(204+2\times 102+2^{2}\right)$$
$$10404=10000\left(204+204+2^{2}\right)$$
$$10404=10000\left(408+2^{2}\right)$$
$$10404=10000\left(408+4\right)$$
$$10404=10000\times 412$$
$$10404=4120000$$
$$\text{false}$$
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