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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