How will (m^2-10m+25) be written in factorised form?

Correct answer: $(m-5)^2$

The direct answer is B: $(m-5)^2$. Begin with the identity $a^2-2ab+b^2=(a-b)^2$. In the given expression, $m^2$ is the square of m, and 25 is the square of 5. Now check the middle term: $-2×m×5=-10m$, exactly as given. Therefore $m^2-10m+25=(m-5)^2$. We can verify by expanding: $(m-5)(m-5)=m^2-5m-5m+25=m^2-10m+25$. A gives $(m+5)^2=m^2+10m+25$, so its middle sign is wrong. C expands to $m^2+15m-250$, not the original expression. D gives $m^2-50m+625$, so both its middle and constant terms are wrong. Memory cue: for a perfect square, take the square roots of the first and last terms, then use the middle sign.