Question

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

Explanation:

Step1: Expand left - hand side

Recall the formula \((a - b)^2=a^{2}-2ab + b^{2}\). For \((x - 4)^2\), where \(a = x\) and \(b = 4\), we have:
\((x-4)^{2}=x^{2}-2\times x\times4 + 4^{2}\)

Step2: Simplify the expansion

Calculate the products and exponents:
\(x^{2}-2\times x\times4+4^{2}=x^{2}-8x + 16\)
Which is equal to the right - hand side of the given equation \(x^{2}-8x + 16\).

Answer:

The equation \((x - 4)^2=x^{2}-8x + 16\) holds true (it is an identity, valid for all real values of \(x\)).