#### Answer

$a^{2}-4ab+4b^{2}$

#### Work Step by Step

Write out the equation
$(a-2b)^{2}$
While you may be tempted to simply square $a$ and $-2b$ this is incorrect. Remember that when an entire expression is squared it is multiply itself by itself when expanding the equation:
$(a-2b)(a-2b)$
Multiply each term in the first polynomial by each term in the second polynomial.
$a^{2}-2ab-2ab+4b^{2}$
$a^{2}-4ab+4b^{2}$