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Factorize:

[tex]x^4 y^6 - 7x^3 y^2 + 14x^3 y^4[/tex]

Answer :

Sure! Let's factorize the expression [tex]\( x^4 y^6 - 7 x^3 y^2 + 14 x^3 y^4 \)[/tex].

1. Identify Common Factors:
- Look for common factors in all the terms. We can see that each term has at least [tex]\( x^3 y^2 \)[/tex] in it. Let's factor that out first.

2. Factor Out the Common Term:
- Extract [tex]\( x^3 y^2 \)[/tex] from each term:
[tex]\[
x^4 y^6 - 7 x^3 y^2 + 14 x^3 y^4 = x^3 y^2 (x y^4 - 7 + 14 y^2)
\][/tex]

3. Simplify Inside the Parentheses:
- Simplify the expression inside the parentheses:
[tex]\[
x y^4 - 7 + 14 y^2
\][/tex]
- Rearrange terms for clarity:
[tex]\[
x y^4 + 14 y^2 - 7
\][/tex]

So, the fully factorized expression is:
[tex]\[
x^3 y^2 (x y^4 + 14 y^2 - 7)
\][/tex]

This is the final factorized form of the given expression.

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Rewritten by : Barada