How to Reduce Binomials

Binomial is also an algebraic equation but it has only two terms. (a+b) It’s  a example of binomial. And the binomial theorem commonly used to expand the binomials to any given power without direct multiplication .Here we are going to learn about how to reducing binomials. Let us see about binomial with examples.

More information about binomials

The following binomial shows, how we can write the binomials using powers
(a + b)⁰ is equal to  1
(a + b)¹ can be written as  a + b
(a + b)² can be written as  a² + 2ab + b²
(a + b)³ can be written as a³ + 3a²b + 3ab² + b³
(a + b)⁴ can be written as  a⁴ + 4a³b + 6a²b² + 4ab³ + b⁴
(a + b)⁵ can be written as  a⁵ + 5a⁴b + 10a³b² + 10a²b³ + 5ab⁴ + b⁵

Example problems for how to reduce binomials:

Example 1:
Reduce  `((x+2)^2)/(x+2)`
Solution:

Step 1: We can write it as an .`((x+2)^2)/(x+2)`

Step 2: And the question can be written as  `((x+2)(x+2))/(x+2)`

Step 3: On both the numerator and denominator, the (x+2) will be cancelled.

Step 4: Therefore, the answer is (x+2).

Example 2:
Reduce 2ab+5yz-ab-3yz+9ab.
Solution:

Step 1: First we need to arrange the terms.

Step 2: So, 2ab-ab+9ab+5yz-3yz.

Step 3: Here, we need to add the terms.

Step 4: Therefore the answer is 10ab+2yz.

Example 3:
Reduce  `((x+7) (x+9))/((x+81)^2 (x+49)^2)`
Solution:

Step 1: It can be written as  `((x+7) (x+9))/((x+81)^2 (x+49)^2)`

Step 2: And, we can write the given question is `((x+7)(x+9))/((x+9)(x+9)(x+7)(x+7))`

Step 3: And Here both the sides the (x+7) and (x+9 ) are canceled.

Step 4: Therefore the answer  is`(1)/((x+9)(x+7))`

Example 4:
Reduce 4ts+6gh-ts-2gh+7ts.
Solution:

Step 1: First we need to arrange the terms.

Step 2: So, 4ts+7ts-ts+6gh-2gh.

Step 3: Here, we need to add the terms.

Step 4: Therefore the answer is 10ts+4gh

Example 5:
Reduce:  `((a+b)^3 (5a))/((a+b) (25))`
Solution:

Step 1: The question can be written as `((a+b)(a+b)(a+b)(5a))/((a+b) (25))`

Step 2: On both the numerator and denominator, the (a+b) and 5 will be canceled.

Step 3: Therefore, the answer is `((a+b)^2 (a))/(5)`

These are the examples of how to reducing binomials.