Which of the following trinomials can be factorised as a perfect square using the identity $a^2+2ab+b^2=(a+b)^2$?

Correct answer: $x^2+10x+25$

The direct answer is A: $x^2+10x+25=(x+5)^2$. To recognize a perfect-square trinomial, identify the first and last terms as squares: $x^2=x^2$ and $25=5^2$. The middle term must equal $2ab$, where $a=x$ and $b=5$. Indeed, $2×x×5=10x$, so the identity gives $x^2+10x+25=(x+5)^2$. Option B has the same first two terms, but 24 is not 25, so it is not a perfect square of this form. In C, the square roots are x and 5, but $2×x×5=10x$, not 8x. In D, although $x^2$ and 24 do not form the needed square pair, the negative middle term would be associated with $(x-5)^2$ only if the constant were 25; it is not. The safe check is to compare the constant with $b^2$ and the middle term with $2ab$.