Factorize

The above question is an old stuff. However, I'm wondering that how many of F.6 students can give correct answer.

Let's use something we are learning to solve it. That is : determinant（行列式）

Click here to read the solution if necessary.

Based on the above result, we can create following questions like

EQ.1　

I was impressed by the result above when I was reading a small mathematics book called “等式的證明” when I was a F.1 (or F.2, I can't remember) student.

Add more condition, we have

EQ.2　

Students, try it if you have time.

I'm so hurry that I skip something (not important thing) in lesson sometimes, and I'd like to post in this forum.

Consider a determinant of order 3 (say), , suppose A, B, C, ..., I are cofactors of a, b, c, ..., i respectively, we know that we can "expand" the determinant along any row or any column, as for example

,
,... etc.

However, if we multiply the cofactors of entries of "other" row (or column), we'll get zero.

For example

,

= 0, ...etc.

In lesson, I said that the proof is simple but I'll not "waste" time to discuss it. Now, let me speak silently in this forum.

To prove , just think about

The result follows because the LHS = 0.

Hope you'll enjoy learning Mathematics and make fun of it.

Also read.