So today,we got back our exam papers,and we found a question marked wrongly and teacher said that it is wrong.We all students do NOT believe this.So here is what happened.
Before reading the next part,this is what we ONLY know (learnt) about rules of special products.
(Under school secondary 2 learning in Singapore)
Rule $1$: $a^2+2ab+b^2=(a+b)^2$
Rule $2$ :$a^2-2ab+b^2=(a-b)^2$
Rule $3$: $a^2-b^2=(a+b)(a-b)$
From the exam paper:
Evaluate $10.2^2-9.8^2$ by using ONLY rules of special products.
Correct solution: $(10.2+9.8)(10.2-9.8)=(20)(0.4)=8$ (Rule $3$)
Student wrong (Marked as wrong) alternate solution: \begin{align*} (10+0.2)^2-(10-0.2)^2 &=[10^2+2(10)(0.2)+0.2^2]-[10^2-2(10)(0.2)+0.2^2]\\&=100+4+0.04-(100-4+0.04)\\&=104.04-96.04\\&=8\end{align*}(Rules $1$ and $2$)
The question did NOT ask for the easiest and fastest way (and both solution uses ONLY rules of special products) to solve but yet why is student solution wrong? Teacher told us,"Aiya, why need to do so complicated one?" yet she did not answer why is the answer wrong. I debated to her so long but to no avail.
Can anybody think of why the student solution is wrong?