How Do I Factor This Expression?

  • MHB
  • Thread starter mathdad
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In summary, factoring is the process of finding what to multiply together to get an expression. It is like "splitting" an expression into a multiplication of simpler expressions. Factoring can also be defined as the opposite of multiplication, or the inverse of division.
  • #1
mathdad
1,283
1
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?
 
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  • #2
Perfect. (Yes)
 
  • #3
Great! Factoring is fun. Can I safely define factoring as the opposite of multiplication?
 
  • #4
I would say division is the inverse of multiplication, but factoring is certainly related to division. For example, we know:

\(\displaystyle a^2-b^2=(a+b)(a-b)\,\therefore\,a-b=\frac{a^2-b^2}{a+b}\)
 
  • #5
Without using math jargon, what is the simplest definition of factoring?
 
  • #6
RTCNTC said:
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.
 
  • #7
MarkFL said:
Finding what to multiply together to get an expression. It is like "splitting" an expression into a multiplication of simpler expressions.

Thank you.
 

FAQ: How Do I Factor This Expression?

Can I factor any expression?

Yes, in most cases, expressions can be factored. However, there are some exceptions where an expression may not be able to be factored.

What is the purpose of factoring an expression?

Factoring an expression can help simplify it and make it easier to work with. It can also help in solving equations and identifying patterns within the expression.

How do I know when an expression can be factored?

There are various methods and techniques for factoring an expression, such as looking for common factors, using the quadratic formula, or using the difference of squares formula. Practice and familiarity with these methods can help determine when an expression can be factored.

What is the difference between factoring and simplifying an expression?

Simplifying an expression involves reducing it to its simplest form by combining like terms and performing operations. Factoring, on the other hand, involves breaking down an expression into smaller parts that can be multiplied together to get the original expression.

Can I factor an expression with variables?

Yes, expressions with variables can also be factored. In fact, factoring is often used in algebra to solve equations with variables.

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