dave wrote:

Please explain how and why you go from (2*x*)² – 2 × 2*x* + 1 = 0 to (2*x* – 1)² .

1. Why?

Our goal is to determine what set of values Statement (1) defines. Statement (1) is a quadratic equation and thus we need to solve it. You may use any method that you like. We solved the equation by factoring.

2. How?

We used the formula (

*a* –

*b*)² =

*a*² –2

*ab* +

*b*² in reverse.

It comes directly from multiplying the two factors in parentheses:

(

*a* –

*b*)(

*a* –

*b*) =

*a**a* –

*b**a* –

*ab* + (-

*b*)(-

*b*) =

*a*² –2

*ab* +

*b*²

In case of the equation we have:

(2

*x* – 1)² = (2

*x*)² – 2 × 2

*x* + 1

**Quote:**

Also in the previous step why is it necessary to separate the terms like that?

We did it to apply the formula, to see what

*a* is and what

*b* is.