# Question #5a96c

Nov 16, 2016

$\left(5 a - 8 b\right) \left(5 a - 8 b\right) = {\left(5 a - 8 b\right)}^{2}$

#### Explanation:

$25 {a}^{2} - 80 a b + 64 {b}^{2}$

This is actually much easier than is appears at first glance.

Note that both $25 \mathmr{and} 64$ are perfect squares.

In ${\left(2 a + 3 b\right)}^{2} = 4 {a}^{2} + 12 a b + 9 {b}^{2}$
$\textcolor{w h i t e}{\times \times \times \times \times \times \times x} \uparrow$
The middle term is double the product of 2 and 3

Check if that is the case here: $\left(5 \times 8\right) \times 2 = 80 \text{ }$ BINGO!

$\left(5 a - 8 b\right) \left(5 a - 8 b\right) = {\left(5 a - 8 b\right)}^{2}$

If you did not spot that, you would need to read it as:

"Find factors of 25 and 64 which ADD to 80"