Question

How do you factor the expression \[2{x^3}y - {x^2}y + 5x{y^2} + x{y^3}\] ?

Answer 1

Hint: We have to find the factor of the given expression \[2{x^3}y - {x^2}y + 5x{y^2} + x{y^3}\] , factorization: It is the process where the original given number is expressed as the product of prime numbers. For this we have to calculate the prime factor of \[2{x^3}y - {x^2}y + 5x{y^2} + x{y^3}\].

Complete step by step solution:
The given expression is as follow ,
\[2{x^3}y - {x^2}y + 5x{y^2} + x{y^3}\],
We have to find the factor of the given expression.
factorization: It is the process where the original given number is expressed as the product of
prime numbers.
Therefore , Factorization of \[2{x^3}y - {x^2}y + 5x{y^2} + x{y^3}\] :
\[
   = 2{x^3}y - {x^2}y + 5x{y^2} + x{y^3} \\
   = xy(2{x^2} - x) + xy(5y + {y^2}) \\
   = xy(2{x^2} - x + 5y + {y^2}) \;
 \]
Hence, we get the required result that is a factor of the given expression \[2{x^3}y - {x^2}y + 5x{y^2} + x{y^3}\] .
So, the correct answer is “$xy(2{x^2} - x + 5y + {y^2})$”.

Note: LCD: Lowest Common Denominator : Lowest common denominator can be found by multiplying the highest exponent prime factors of the denominator . lowest common denominator is also known as Least common multiple and this can be calculated in two ways ; with the help of greatest common factor (GCF), or multiplying the prime factors with the highest exponent factor. Prime factorization: It’s the process where the original given number is expressed as the product of prime numbers.