MHB How Do I Factor This Expression?

[mathdad]

Factor the expression.

3(x + h)^4 - 48(x + h)^2

I believe I can factor out 3(x + h)^2.

If so, we then have the following:

3(x + h)^2[(x + h)^2 - 16]

I think (x + h)^2 - 16 is the difference of two perfect squares.

If so, then it factors out to be [(x + h) - 4][(x + h) + 4].

Answer: 3(x + h)^2[(x + h) - 4][(x + h) + 4].

Correct?

 

[MarkFL]

Perfect. (Yes)

 

[mathdad]

Great! Factoring is fun. Can I safely define factoring as the opposite of multiplication?

 

[MarkFL]

I would say division is the inverse of multiplication, but factoring is certainly related to division. For example, we know:

$$a^2-b^2=(a+b)(a-b)\,\therefore\,a-b=\frac{a^2-b^2}{a+b}$$

 

[mathdad]

Without using math jargon, what is the simplest definition of factoring?

 

[MarkFL]

Without using math jargon, what is the simplest definition of factoring?

Finding what to multiply together to get an expression. It is like "splitting" an expression into a multiplication of simpler expressions.

 

[mathdad]

Finding what to multiply together to get an expression. It is like "splitting" an expression into a multiplication of simpler expressions.

Thank you.