Replace terms within a polynomial function with other terms?

Questions
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1

Hi all,

I would like to ask if there’s a way to replace a few terms within a polynomial function into another term.

For example of my work, I have a term of

 1 - 6 \[Lambda]^2 + 10 \[Lambda]^4

and I would like to replace the term

-\[Lambda]^2

within the the polynomial into X^2,

so that the final answer should be =

1 + 6 X + 10 X^2

Thank you,

Regards,
Syed

2

In[1]:= eq1 = 1 - 6 [Lambda]^2 + 10 [Lambda]^4

Out[1]= 1 - 6 \[Lambda]^2 + 10 \[Lambda]^4

In[2]:= eq1 /. Power[\[Lambda], n_] -> (-x)^(n /2)

Out[2]= 1 + 6 x + 10 x^2

In order to find out what expression Mathematica is using and which you have to replace you can use

FullForm[eq1]
3

In general, one can use the function Eliminate:

Eliminate[{f == 1 - 6 \[Lambda]^2 + 10 \[Lambda]^4, -\[Lambda]^2 == x}, \[Lambda]]
Solve[%, f]

to eliminate a variable (lambda in your case) from multiple equations (2 in your case)…