Simple Factor Multiplication

Multiplying is simple.

What is 4 x 3?
Answer is 4 x 3 = 12.

Simple?
Sure it is.

How about y(y - 1)?
Answer is y² - y.

Again simple? Sure.

But how about (y + 1)(2y + 3)?
Many of you may find this simple and basic.

But you may still come across some who did not grasp this factor multiplication.
Mistake still occur for this maths operation involving factors.

What is the mistake commonly seen?

(y + 1)(2y + 3) is given as (y)(2y) + (1)(3).
First term multiply by first term, second one multiply with the second one. That's all.
This is incorrect mathematically.

This is a misconception of what multiplication does.

Let me explain.
(y + 1)(2y + 3) can be interpreted as (y)(2y + 3) plus (1)(2y + 3).
This is key to this form of maths operation.

The second term (2y + 3) is multiplied by the first term "y" of the first factor (y + 1).
(2y + 3) is next multiplied by the second term "1" of the first factor.
The result of these two operations are then added up, since it is y add 1 (as reflected in the first factor).

The correct answer is then:
(y + 1)(2y + 3)
= (y)(2y) + (y)(3) + (1)(2y) + (1)(3)
= 2y² + 3y + 2y + 3
= 2y² + 5y + 3

Learn from the mistake, and do not repeat it.
This is the basic concept in learning from mistakes. They are our teacher.

Remember, maths is interesting!
A twist can be destructive or constructive.
That is where maths is special and challenging.

Cheers! :-)
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