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

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.

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 ?

Answer:

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?

Answer: No

Question :

Do we have any common variable in group 2?

Answer: Yes,that is x.

Question :

Do we have any common number in group 1?

Answer:

Yes, we can split 8 as multiple of 4.

Question :

Do we have any common number group 2?

Answer:

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 2a**³ - 3a****²b + 2****a****²c **

**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)

**Example 5:**

Factorize 9x² - 24xy + 16y²

**Solution:**

**We have x****² as the first term and y****² as the last term.Since there are only three terms.We can compare the given question with the algebraic identity a****² - 2ab + b****²**

** = 9x² - 24xy + 16y²**

= 3**² **x**² - 2(3x) (4y) + 4****² ****y****²**

** = (3 x)² - 2(3x) (4y) + (4 y)²**

** = (3x - 4y)**

- Factoring quadratic equations when the coefficient of x² is not 1
- Solving quadratic equation using c
- ompleting the square method
- Solving quadratic equation by using quadratic formula
- Practical problem using quadratic equations

To know more about the topic please click here.

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