Question

How do you factor completely: `100x^2 – 1`?

Answer 1

`color(blue)((10x-1)(10x+1)`

Explanation:

`color(blue)(a^2-b^2 = (a-b)(a+b)`

The same property can be applied for the above expression:

`100x^2-1`, here `color(blue)(a=10x, b=1`

The expression can now be factorised as:
`100x^2-1 = (10x)^2 - 1^2 = color(blue)((10x-1)(10x+1)`