Question

May someone teach me how to use the magic x method to factor the quadratic 16x^2-36 step by step?

Answer 1

The difference of squares will factor into conjugates like this:


`\rm a^2-b^2\quad=\quad (a-b)(a+b)`

In order to apply this property,
we must first write both terms as perfect squares.

36 is 6^2, that's easy enough to rewrite as a perfect square.
The other one is a little trickier.
16 is 4^2. From there we'll group the 4^2 and x^2 into a single square using an exponent property,


`\rm 16x^2=4^2x^2=(4x)^2`

So our expression looks like this,


`\rm 16x^2-36`

`\rm (4x)^2-6^2`

Applying our difference of squares rule,


`\rm (4x)^2-6^2=(4x-6)(4x+6)`

Hope that helps! :)