Reena claims that 25p² − 20p + 4 factorises as (5p − 2)². Which is the correct expansion of (5p − 2)² to verify her claim?

Correct answer: 25p² − 20p + 4

The correct answer is A: (5p − 2)² = 25p² − 20p + 4. Start with the identity (a − b)² = a² − 2ab + b². Here a = 5p and b = 2. Therefore, a² = 25p², −2ab = −2 × 5p × 2 = −20p, and b² = 4. Combining these terms gives 25p² − 20p + 4, exactly the expression in the question. Option A is correct because all three terms match. Option B omits the middle term, so it is not the square of a binomial. Option C has an incorrect middle coefficient; the product must be doubled. Option D has the wrong sign because squaring a difference produces a negative middle term. Memory cue: for (a − b)², remember “square, minus double product, square.”