How do you factor the expression 25x^2 – 16 by using the difference of two squares method?

Answer 1

Recall the difference of squares: a² - b² = (a - b)(a+b)

25x² - 16 = (5x)² - 4² = (5x - 4)(5x + 4)

Answer 2

You can re-write 25x² as (5x)² and you can re-write 16 as (4)²

So now 25x² - 16 = (5x)² - 4⁴ (Notice it is now the difference (subtraction) of two perfect squares.

This factors into (5x-4)(5x+4)