Question

which expression is equivalent to $(5x - 4)^2$?

1. $25x^2 + 16$
2. $25x^2 - 20x + 16$
3. $25x^2 - 40x + 16$
4. $25x^2 + 40x + 16$

Explanation:

Step1: Apply square of binomial formula

The formula for \((a - b)^2 = a^2 - 2ab + b^2\). Here, \(a = 5x\) and \(b = 4\).

Step2: Calculate each term

• \(a^2 = (5x)^2 = 25x^2\)
• \(2ab = 2(5x)4 = 40x\)
• \(b^2 = 4^2 = 16\)

Step3: Combine terms

\((5x - 4)^2 = 25x^2 - 40x + 16\)

Answer:

1. \(25x^2 - 40x + 16\)