Respuesta :

 15x2y2+3x3y+75x4 Final result : 3x2 • (25x2 + xy + 5y2)

Step by step solution :Step  1  :Equation at the end of step  1  : (((15•(x2))•(y2))+((3•(x3))•y))+(3•52x4) Step  2  :Equation at the end of step  2  : (((15•(x2))•(y2))+(3x3•y))+(3•52x4) Step  3  :Equation at the end of step  3  : (((3•5x2) • y2) + 3x3y) + (3•52x4) Step  4  :Step  5  :Pulling out like terms :

 5.1     Pull out like factors :

   75x4 + 3x3y + 15x2y2  =   3x2 • (25x2 + xy + 5y2) 

Trying to factor a multi variable polynomial :

 5.2    Factoring    25x2 + xy + 5y2 

Try to factor this multi-variable trinomial using trial and error 

 Factorization fails

Final result : 3x2 • (25x2 + xy + 5y2)

anuksha0456

The factorized form of the algebraic expression 15x²y² - 3x³y + 75x⁴ is 3x²(5y² - xy + 15x²).

What is the factorization of algebraic expressions?

Factorization of algebraic expressions is a process to break the expression and show it as a product of two or more smaller expressions by grouping and taking the greatest common factor out of the groups.

How to solve the question?

In the question, we have been asked to factor the expression 15x²y² - 3x³y + 75x⁴ completely.

We know that factorization is the process of breaking the expression into smaller expressions.

We first try to find the greatest common factor among the three terms provided in the expression.

First, we will go with the numerical part.

We have 15, -3, and 75.

The greatest common factor for these three is 3.

No, we will go with the variable part.

We have x²y², x³y, and x⁴.

The greatest common factor for these three is x².

Thus, the greatest common factor for the expression is 3x²

.

Taking 3x² common throughout, we get:

3x²(5y² - xy + 15x²), which is the required factored form.

Learn more about the factorization of algebraic expressions at

https://brainly.com/question/22048677

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