Learn factorization by a suitable formula || Easy examples and a simple explanation

In algebra, the practice of factorization by a suitable formula often is the essential portion of mathematics for class 5 to class 8. Factorization by a suitable formula for class 6 to 8 students, often makes confused to students how to solve factorization by using suitable formula. In this article, we learn factorization by a suitable formula with easy examples and a simple explanation.

What are the easy and important steps of factorization by a suitable formula?

Today we will teach you easy and important steps of factorization by a suitable formula with examples for class 8. You will learn them step by step.

Step 1: Must recognize which formula can be used for the given question.

Step 2: After that, solve it according to the formula.

A simple example of factorization by a suitable formula:

Here we are going to teach you a simple example of factorization by a suitable formula. You can easily learn factorization with these examples. We will help you to solve factorization along with algebraic formulas.

Examples of factorization by a suitable formula of (a)2-(b)2 =  (a-b)(a+b).

Some algebraic factorization by a suitable formula is solve with (a)2-(b)2 =  (a-b)(a+b) formula. We will show you some examples of (a)2-(b)2 =  (a-b)(a+b) along with the solution.

Example 1:

Factorize 206x194 with a suitable formula.

Now we know that, (a)2-(b)2 =  (a-b)(a+b)

206 can be written as (200+6) and 194 can be written as (200-6)

So, 206x194 will become,

(200+6)(200-6)

(200) 2-(6)2 

40000-36

 39,964 ANS

Example 2:

Factorize 85x75 by a suitable formula

(80+5)(80-5)

We know that, (a)2-(b)2 =  (a-b)(a+b)

(80)2-(5)2

6400-25

6375 ANS.

10 problems Factorization with suitable formula of (a)2-(b)2=(a-b)(a+b) for practice:

1. 55x45

2. 68x52

3. 97x83

4. 104x96

5. 210x190

6. 250x150

7. 49x31

8. 33x27

9. 35x25

10. 92x88

Examples of factorization by a suitable formula of (a+b)2=(a2+2ab+b2)

In algebra, some problems are factorized with the suitable formula of (a+b)2 =(a2+2ab+b2). We will do some examples of factorization with a suitable formula of (a+b)2=(a2+2ab+b2).

Example 1:

144a2+144ab+36b2 

We know that, (a+b)2 =(a2+2ab+b2)

144a2+144ab+36b2 is the in format of (a2+2ab+b2).

→ (12a)2+(2)(12a)(6b)+(6b)2

→Take the first and the last term

(12a+6b) 2 ANS

Example 2:

49a2+70ab+25b2       

We know that, (a+b)2 =(a2+2ab+b2)

→(7a)2+(2)(7a)(5b)+(5b)2

→(7a+5b)2 ANS.

10 problems of factorization with suitable formula of (a+b)2 =(a2+2ab+b2) for practice:

1. 9a2+30ab+25b

2. 25a2+100ab+100b2       

3. 9a2+60ab+100b2 

4. 196a2+140ab+25b2       

5. 196a2+168ab+36b2       

6. 49a2+70ab+25b2 

7. 16a2+120ab+225b2       

8. 9a2+96ab+256b2 

9. 49a2+70ab+25b2 

10. 100a2+250ab+225b2 

10 examples of factorization by a suitable with (a-b)2=(a2-2ab+b2) formula:

(a-b)2=(a2-2ab+b2) also comes under factorization by a suitable formula. The factorization with (a-b)2=(a2-2ab+b2) formula is same as the factorization with (a+b)2=(a2+2ab+b2) formula. There is just difference of sign between the factorization with (a+b)2=(a2+2ab+b2) and (a-b)2=(a2-2ab+b2) formulas. We will provide you 10 examples of factorization with (a-b)2=(a2-2ab+b2) formula. The steps are the same as described above. Just change the sign.

Examples:

1. 81a2-90ab+25b

2. 169a2-260ab+100b2     

3. 9a2-108ab+324b2

4. 36a2-180ab+225b2        

5. 196a2-364ab+169b2     

6. 49a2-140ab+100b2        

7. 4a2-60ab+225b2  

8. 100a2-320ab+256b2     

9. 49a2-84ab+36b2  

10. 100a2-240ab+144b2  

Examples of factorization by a suitable formula of (a) 3+(b)3=(a-b)(a2+ab+b2)

Factorization by a suitable formula can also be executed by (a) 3+(b)3=(a-b)(a2+ab+b2) formula. This factorization is helpful for classes 8, 9, 10, and even for university students. We learn some factorization examples by using (a)3+(b)3=(a-b)(a2+ab+b2) formula. There are some steps which we have to follow them.

Step 1: You have to take cube root or 3√ of the given variables

Step 2: Put all the values according to the above-mentioned formula.

Let’s learn the factorization with (a) 3+(b)3=(a-b)(a2+ab+b2) formula with an easy example.

Example 1:

64a3+125y3

→The above question is in the format of (a)3+(b)3=(a-b)(a2+ab+b2) so →we will take the cube root or 3√  of 64a3 and 125y3

→(4a)3+(5y)3

Now put the values in (a-b)(a2+ab+b2)

We will get the final answer,

→ (4a)3+(5y)3=(4a-5y)(16a2+20ay+25y2) ANS.

Example 2:

343a3-512y3

∴ (7a)3-(8y)3

→Now put the values in (a)3-(b)3=(a+b)(a2-ab+b2)

→(7a)3+(8y)3=(7a+8y)(49a2-56ay+64y2) ANS.

10 problems of factorization with suitable formula of (a)3+(b)3=(a-b)(a2+ab+b2)  and (a)3-(b)3=(a+b)(a2-ab+b2) for practice:

Here we will provide you 10 problems of factorization with suitable formula of (a)3+(b)3=(a-b)(a2+ab+b2)  and (a)3-(b)3=(a+b)(a2-ab+b2) for practice. You can practice them and easily learn factorization.

1. 1000 a3+27y3

2. 1331a3+8y3

3.729a3+125y3

4. 216a3+343y3

5. 512a3+27y3

6.1331a3-8y3

7. 125a3-343y3

8. 8000a3-125y3

9. 216a3-27y3

10. 1728a3-343y3

Hope you would have clearly understood factorization by a suitable formula with easy examples and a simple explanation. Still, if you feel any confusion then comment to us. 

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