# Solving a question by using special products (Students debate to Teacher)

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?

• Your solution is correct. She's butt-hurt because she failed to account for other possible correct solutions. – Git Gud Mar 4 '15 at 16:29
• The teacher is silly ! Both are equivalent things done in two ways! – Shakul Pathak Mar 4 '15 at 16:33
• The unexpected answer is well within the realm of correct. This teacher is out-of-bounds. I teach; I also like unexpected answers that work and strongly encourage this kind of thinking. – ncmathsadist Mar 4 '15 at 19:59
• I think that the second approach is arguably better as it demonstrates knowledge of two of the three rules rather than just one. If you really want to split hairs you could argue that since the question refers to "rules", i.e. plural, the first answer is not even valid as it only uses a single rule! The question should have been disambiguated, e.g. "using exactly one rule", or "using one or more rules". The fact that this was not done indicates a lack of rigour. – Marconius Jul 9 '15 at 12:07
• Whoops,forgot to look back at this post.This is solved.We got our exam marks :D – ministic2001 Oct 18 '15 at 12:45