What is the simplified form of the function 7(x^3+4x)^6(3x^2+4)?

In summary, simplifying a function means manipulating it to make it easier to understand and work with. This is important because it can make the function easier to analyze, evaluate, and solve. To simplify a function, combine like terms, factor, and reduce fractions. Any function can be simplified using algebraic techniques, but some may have simpler forms than others. Simplifying a function is not the same as solving it, as solving involves finding specific values that make the function true.
  • #1
h_k331
33
0
According to my text 7(x^3+4x)^6(3x^2+4) simplifies to:

7x^6(x^2+4)^6(3x^2+4)

But it seems to me it should simplify to:

7x(x^2+4)^6(3x^2+4)

What am I missing here?

hk
 
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  • #2
h_k331 said:
According to my text 7(x^3+4x)^6(3x^2+4) simplifies to:

7x^6(x^2+4)^6(3x^2+4)

But it seems to me it should simplify to:

7x(x^2+4)^6(3x^2+4)

What am I missing here?

hk

[tex](x^3+4x)^6=[x(x^2+4)]^6=x^6(x^2+4)^6[/tex]
 
  • #3
Ah, now I understand. Thank you saltydog.

hk
 

1. What does it mean to simplify a function?

Simplifying a function means to manipulate the function in order to make it easier to understand and work with. This typically involves combining like terms, factoring, and reducing fractions.

2. Why is it important to simplify a function?

Simplifying a function can make it easier to analyze and evaluate, as well as make it more efficient to solve for certain values or variables. Simplifying can also help to identify patterns and relationships within the function.

3. How do you simplify a function?

To simplify a function, start by combining like terms and removing any unnecessary parentheses. Then, factor the resulting expression to find common factors that can be reduced. Finally, check for any remaining terms that can be combined or simplified further.

4. Can any function be simplified?

Yes, any function can be simplified using algebraic techniques. However, some functions may have simpler forms than others and may not require as many steps to simplify.

5. Is simplifying a function the same as solving it?

No, simplifying a function involves manipulating the expression in order to make it easier to work with. Solving a function means finding the value or values of the variable that make the function true.

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