Possible webpage title: How to Factorize x^5y^2 + x^2y^5 in Algebra

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In summary, factorization is the process of breaking down an algebraic expression into simpler terms by identifying common factors. To factorize an expression, you need to look for common factors in each term. The degree of a factorized expression is the highest power of the variable that appears in any of the factors. The expression x^5y^2 + x^2y^5 can be further factorized using the difference of squares formula, giving us the final factorization of xy(x^2 + y^2)(x^2 - y^2). Factorization is important because it allows us to solve equations, simplify expressions, and identify patterns in mathematics. It also helps us in finding common factors and simplifying complex expressions, and
  • #1
alpha01
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[SOLVED] factorizing x^5y^2 + x^2y^5

factorize:


[tex]x^5y^2 + x^2y^5[/tex]



The Attempt at a Solution




I have attempted to use difference of two squares by re-arranging as:


[tex]x^5y^2 + y^5x^2[/tex]

but this doesn't get me anywhere
 
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  • #2
Take out common things.
[tex]x^2y^2(x^3+y^3)[/tex]

Now use the expansion for [tex](x^3+y^3)[/tex]
 
  • #3
easy. thanks ;)
 

1. What is factorization?

Factorization is the process of breaking down an algebraic expression into simpler terms. This is done by identifying common factors and rewriting the expression as a product of these factors.

2. How do I factorize an expression?

To factorize an expression, you need to look for common factors in each term. In the expression x^5y^2 + x^2y^5, both terms have a common factor of xy. So, we can factor out xy to get xy(x^4 + y^4).

3. What is the degree of a factorized expression?

The degree of a factorized expression is the highest power of the variable that appears in any of the factors. In the expression x^5y^2 + x^2y^5, the degree is 7 (x^5y^2 has a degree of 7).

4. Can I factorize x^5y^2 + x^2y^5 further?

Yes, the expression can be further factorized by using the difference of squares formula: x^4 + y^4 = (x^2 + y^2)(x^2 - y^2). This gives us the final factorization of xy(x^2 + y^2)(x^2 - y^2).

5. Why is factorization important?

Factorization is important because it allows us to solve equations, simplify expressions, and identify patterns in mathematics. It also helps us in finding common factors and simplifying complex expressions. In some cases, factorization can also help us in understanding real-world problems and making mathematical models.

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