a2 b2 formula is one of the most used formulae in mathematics. The formula is highly useful in further studies, and hence many questions, directly or indirectly, can be asked from this and related formulae in CBSE or ICSE exams. So, in this article, we have provided a2 b2 formula as well as other formulae which are also frequently asked in exams. Hence, we advise you to read the full article if you want to score good marks in your exam. So, without any further delay, let’s get started.

In this article, you will get to know the following formulae

1) a^{2} + b^{2}

2) a^{2} – b^{2}

3) a^{2} + b^{2} + c^{2}

**a2 b2 formula with examples || a2 b2 formula with answers**

In this section, we give you the a2 b2 formula with proof

a^{2} + b^{2} = (a+b)^{2} – 2ab

Alternate a2 b2 formula:

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

**a2 b2 Formula Proof : **

As we know that :

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

After shifting sides, we get :

a^{2} +b^{2 }= (a+b)^{2} – 2ab

Proof of alternate formula

As we know that

(a-b)^{2 }= a^{2} + b^{2} – 2ab

After shifting sides, we get:

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

Hence:

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

**a2 – b2 Formula Proof :**

In this section, we provide you a2 b2 formula with proof

Let us multiply (a + b) and (a – b)

(a + b) * (a – b) = a*a – a*b +a*b – b*b

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

after cancelling +ab and –ab we get

(a + b) (a – b) = a^{2} – b^{2}

Hence :

a^{2} – b^{2} = (a + b) (a – b)

**a2 b2 c2 formula**

In this section, we provide you the a2 b2 c2 formula with proof:

(a + b + c)^{2} = (a + b + c)*( a + b + c)

Opening the brackets

(a + b + c)^{2} = a*a + a*b + a*c + b*a + b*b + b*c + c*a + c*b + c*c

(a + b + c)^{2} = a^{2} + b^{2} + c^{2} + 2ab + 2bc + 2ca

(a + b + c)^{2} = a^{2} + b^{2} + c^{2} + 2(ab + bc + ca)

After shifting sides, we get:

(a + b + c)^{2} – 2(ab + bc + ca) = a^{2} + b^{2} + c^{2}

Hence:

a^{2} + b^{2} + c^{2} = (a + b + c)^{2} – 2(ab + bc + ca)

### a2 b2 formula questions

In this section, we would like you to practice the following questions

**(i) if a + b = 5 and ab = 6, find a ^{2} + b^{2}**

**(ii) if a + b = 11 and and a – b = 1, find a ^{2} – b^{2}**

**(iii) if a + b + c = 11 and ab = 6, bc = 18 and ca = 12, find a ^{2} + b^{2} + c^{2}**

### a2 b2 formula answers

In This section, we provide you with the answers of the above questions

(i) 13

(ii) 11

(iii) 49

Frequently Asked Questions (FAQs) about a2 b2 formula:

**Q1) Factorise a-b-a2+b2**

Ans)

a – b – a^{2} + b^{2}

= a – b – (a^{2} – b^{2})

= (a – b) – (a + b) (a – b)

= (a – b) {1 – (a + b)}

= (a – b) {1 – a – b}

**Q2) a2 b2 is equal to**

Ans)

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

and

a^{2} – b^{2} = (a + b) (a – b)

**Q3) a2+ b2 formula**

Ans)

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

So Thats it.

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