Question

1. $(x - 4)^2 = x^2 - 8x + 16$

Explanation:

Step1: Recall the formula for squaring a binomial

The formula for \((a - b)^2\) is \(a^2 - 2ab + b^2\) (where \(a=x\) and \(b = 4\) in this case).

Step2: Apply the formula to \((x - 4)^2\)

Substitute \(a=x\) and \(b = 4\) into the formula \(a^2 - 2ab + b^2\):
\(x^2-2\times x\times4 + 4^2=x^2-8x + 16\)
Which is exactly the right - hand side of the given equation \((x - 4)^2=x^2-8x + 16\). So the equation is an identity (it holds for all real values of \(x\)).

Answer:

The equation \((x - 4)^2=x^2-8x + 16\) is an identity (holds for all real \(x\)).