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).

^{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}=(a^{2}+2ab+b^{2})

^{2}=(a

^{2}+2ab+b

^{2})

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

Example 1:

144a^{2}+144ab+36b^{2 }

We know that, (a+b)^{2 }=(a^{2}+2ab+b^{2})

144a^{2}+144ab+36b^{2} is the in format of (a^{2}+2ab+b^{2}).

→ (12a)^{2}+(2)(12a)(6b)+(6b)^{2}

→Take the first and the last term

(12a+6b)^{ 2 }ANS

Example 2:

49a^{2}+70ab+25b^{2 }

We know that, (a+b)^{2 }=(a^{2}+2ab+b^{2})

→(7a)^{2}+(2)(7a)(5b)+(5b)^{2}

→(7a+5b)^{2 }ANS.

# 10 problems of factorization with suitable formula of (a+b)^{2 }=(a^{2}+2ab+b^{2})
for practice:

1. 9a^{2}+30ab+25b^{}

2. 25a^{2}+100ab+100b^{2 }

3. 9a^{2}+60ab+100b^{2 }

4. 196a^{2}+140ab+25b^{2 }

5. 196a^{2}+168ab+36b^{2 }

6. 49a^{2}+70ab+25b^{2 }

7. 16a^{2}+120ab+225b^{2 }

8. 9a^{2}+96ab+256b^{2 }

9. 49a^{2}+70ab+25b^{2 }

10. 100a^{2}+250ab+225b^{2 }

**10 examples of factorization by a
suitable with (a-b)**^{2}=(a^{2}-2ab+b^{2})
formula:

^{2}=(a

^{2}-2ab+b

^{2}) formula:

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

Examples:

1. 81a^{2}-90ab+25b^{}

2. 169a^{2}-260ab+100b^{2 }

3. 9a^{2}-108ab+324b^{2 }

4. 36a^{2}-180ab+225b^{2 }

5. 196a^{2}-364ab+169b^{2 }

6. 49a^{2}-140ab+100b^{2 }

7. 4a^{2}-60ab+225b^{2 }

8. 100a^{2}-320ab+256b^{2 }

9. 49a^{2}-84ab+36b^{2 }

10. 100a^{2}-240ab+144b^{2 }

**Examples of factorization by a suitable
formula of (a)**^{ 3}+(b)^{3}=(a-b)(a^{2}+ab+b^{2})

^{ 3}+(b)

^{3}=(a-b)(a

^{2}+ab+b

^{2})

Factorization by a suitable formula can also be executed by (a)^{ 3}+(b)^{3}=(a-b)(a^{2}+ab+b^{2})
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)(a^{2}+ab+b^{2})
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)(a^{2}+ab+b^{2})
formula with an easy example**.

Example 1:

64a^{3}+125y^{3}

→The above question is in the format of (a)^{3}+(b)^{3}=(a-b)(a^{2}+ab+b^{2})
so →we will take the cube root or ^{3}√ of 64a^{3 }and 125y^{3}

→(4a)^{3}+(5y)^{3}

Now put the values in (a-b)(a^{2}+ab+b^{2})

We will get the final answer,

→ (4a)^{3}+(5y)^{3}=(4a-5y)(16a^{2}+20ay+25y^{2})
ANS.

Example 2:

343a^{3}-512y^{3}

∴ (7a)^{3}-(8y)^{3}

→Now put the values in (a)^{3}-(b)^{3}=(a+b)(a^{2}-ab+b^{2})

→(7a)^{3}+(8y)^{3}=(7a+8y)(49a^{2}-56ay+64y^{2})
ANS.

**10 problems of factorization
with suitable formula of (a)**^{3}+(b)^{3}=(a-b)(a^{2}+ab+b^{2})
and (a)^{3}-(b)^{3}=(a+b)(a^{2}-ab+b^{2})
for practice:

^{3}+(b)

^{3}=(a-b)(a

^{2}+ab+b

^{2}) and (a)

^{3}-(b)

^{3}=(a+b)(a

^{2}-ab+b

^{2}) for practice:

Here we will provide you 10 problems of factorization with
suitable formula of (a)^{3}+(b)^{3}=(a-b)(a^{2}+ab+b^{2})
and (a)^{3}-(b)^{3}=(a+b)(a^{2}-ab+b^{2})
for practice. You can practice them and easily learn factorization.

1. 1000 a^{3}+27y^{3}

2. 1331a^{3}+8y^{3}

3.729a^{3}+125y^{3}

4. 216a^{3}+343y^{3}

5. 512a^{3}+27y^{3}

6.1331a^{3}-8y^{3}

7. 125a^{3}-343y^{3}

8. 8000a^{3}-125y^{3}

9. 216a^{3}-27y^{3}

10. 1728a^{3}-343y^{3}

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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