Question #5a96c

1 Answer
Nov 16, 2016

Answer:

#(5a-8b)(5a-8b) = (5a-8b)^2#

Explanation:

#25a^2-80ab+64b^2#

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

Note that both #25 and 64# are perfect squares.

In #(2a+3b)^2 = 4a^2 +12ab +9b^2#
#color(white)(xxxxxxxxxxxxxxx)uarr#
The middle term is double the product of 2 and 3

Check if that is the case here: #(5xx8) xx 2 = 80" "# BINGO!

#(5a-8b)(5a-8b) = (5a-8b)^2#

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

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