## HOW TO FACTOR TRINOMIALS WITH 2 DIFFERENT VARIABLES

On this page "how to factor trinomials with 2 different variables",we are going see clear explanation of factoring trinomials with two different variables.

## How to factor trinomials with 2 variables by grouping?

Grouping means factor out the common terms from the group.Let us see some example problems to understand the topic factoring polynomials with two variables.

## How to factor trinomials with 2 different variables

Factoring polynomials can be done by the following methods

(i) Factor the common term

(ii) Factor using algebraic identities

Example 1:

Factor pq - pr - 3ps

Solution:

= pq - pr - 3ps

To factor the above algebraic expression,first we have ask a question for ourself

Question :

Do we find any common term in the above algebraic expression ?

Yes, we have " p" in all three terms. So the answer is p (q - r- 3s)

Example 2:

Factor 4a - 8b + 5ax - 10bx

Solution:

= 4a - 8b + 5ax - 10bx

We have 4 terms in the given algebraic expression.Now we are going to split into two groups.

4a and -8b are in one group (Group 1)

5ax and -10bx are in the other group(Group 2)

Question :

Do we have any common variable in group 1?

Question :

Do we have any common variable in group 2? Question :

Do we have any common number in group 1?

Yes, we can split 8 as multiple of 4.

Question :

Do we have any common number group 2?

Yes, we can split 10 as multiple of 5. Factor out the common term So the factors are (a - 2b) (4 + 5x)

So the answer is p (q - r- 3s)

Example 3:

Factor 2a³ - 3a²b + 2a²c

Solution:

= 2a³ - 3a²b + 2a²c

Question :

Do we find any common variable or number in all three terms?

Answer: yes,we have a² in all three terms.

= a² (2a - 3b + 2c)

Example 4:

Factor 10x³ - 25x⁴ y

Solution:

= 10x³ - 25 x⁴ y

Question :

Do we find any common variable or number in all three terms?

Answer: yes,we have x³ and for number we can split both 10 and 25 as the multiple of 5.So we have 5x³ as common term.

= 5x³ (2x - 5xy)

## How to factor trinomials with 2 different variables using algebraic identities

Example 5:

Factorize 9x² - 24xy + 16y²

Solution:

We have x² as the first term and y² as the last term.Since there are only three terms.We can compare the given question with the algebraic identity a² - 2ab + b²

= 9x² - 24xy + 16y²

= 3² x² - 2(3x) (4y) + 4² y²

= (3 x)² - 2(3x) (4y) + (4 y)²

= (3x - 4y)²

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