# How do you multiply (7-2sqrt3)^2?

Jun 7, 2015

Problem: Multiply ${\left(7 - 2 \sqrt{3}\right)}^{2}$

This is an example of the Square of a Difference, in which

${\left(a - b\right)}^{2} = {a}^{2} - 2 a b + {b}^{2}$.

$a = 7$
$b = 2 \sqrt{3}$

${\left(7 - 2 \sqrt{3}\right)}^{2} = {7}^{2} - 2 \times 7 \times 2 \sqrt{3} + {\left(2 \sqrt{3}\right)}^{2}$ =

$49 - 28 \sqrt{3} + \left(4 \times 3\right)$ =

$49 - 28 \sqrt{3} + 12$ =

$61 - 28 \sqrt{3}$