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) a2 + b2
2) a2 – b2
3) a2 + b2 + c2
a2 b2 formula with examples || a2 b2 formula with answers
In this section, we give you the a2 b2 formula with proof
a2 + b2 = (a+b)2 – 2ab
Alternate a2 b2 formula:
a2 + b2 = (a-b)2 + 2ab
a2 b2 Formula Proof :
As we know that :
(a+b)2 = a2 +b2 +2ab
After shifting sides, we get :
a2 +b2 = (a+b)2 – 2ab
Proof of alternate formula
As we know that
(a-b)2 = a2 + b2 – 2ab
After shifting sides, we get:
a2 + b2 = (a-b)2 + 2ab
Hence:
(a + b)2 – 2ab = a2 + b2 = (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) = a2 – ab + ab – b2
after cancelling +ab and –ab we get
(a + b) (a – b) = a2 – b2
Hence :
a2 – b2 = (a + b) (a – b)
a2 b2 c2 formula
In this section, we provide you with 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 = a2 + b2 + c2 + 2ab + 2bc + 2ca
(a + b + c)2 = a2 + b2 + c2 + 2(ab + bc + ca)
After shifting sides, we get:
(a + b + c)2 – 2(ab + bc + ca) = a2 + b2 + c2
Hence:
a2 + b2 + c2 = (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 a2 + b2
(ii) if a + b = 11 and and a – b = 1, find a2 – b2
(iii) if a + b + c = 11 and ab = 6, bc = 18 and ca = 12, find a2 + b2 + c2
(iv) if a=13 and ab=39, find a2 + b2
(v) if ab = 64 and a/b=16, find a2 + b2 and a2 – b2
See also: a3 + b3 formula
a2 b2 formula answers
In This section, we provide you with the answers to the above questions
(i) 13
(ii) 11
(iii) 49
(iv) 178
(v) a2 + b2 = 272, a2 – b2 = 240
Frequently Asked Questions (FAQs) about a2 b2 formula:
Q1) Factorise a-b-a2+b2
Ans)
a – b – a2 + b2
= a – b – (a2 – b2)
= (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 = a2 + b2 = (a – b)2 + 2ab
and
a2 – b2 = (a + b) (a – b)
Q3) a2+ b2 formula
Ans)
(a + b)2 – 2ab = a2 + b2 = (a – b)2 + 2ab
So That’s it.
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