Which of the following expressions can be factorised as a perfect square using the identity a^2 + 2ab + b^2?

Correct answer: x^2 + 10x + 25

The correct answer is A: x^2 + 10x + 25 = (x + 5)^2. In the identity a^2 + 2ab + b^2, take a = x and b = 5. Then a^2 = x^2, 2ab = 2(x)(5) = 10x, and b^2 = 25. Thus all parts match exactly. Option B has the correct first two terms but its constant is 20 instead of 25, so it is not a perfect square of this form. Option C has the correct square terms but a negative middle term; it equals (x − 5)^2 and uses the difference identity. Option D has 5x rather than the required 10x, so its middle term is too small. The safest check is to identify the square roots of the first and last terms and then verify that twice their product gives the middle term, including its sign.