What is the formula of A plus B plus C whole Square (a + b + c)2
A plus B plus C whole Square formula is an algebraic identity which is used to find the sum of squares of the three numbers. The expression of this A plus B plus C ka whole square formula is (a + b + c)2 = a2 + b2 + c2 + 2(ab + bc + ca). Read about a b c whole square.
How to derive A plus B plus C the whole square ka formula
Lets understand this (a + b + c)2 Formula in details. this formula is the sum of the squares of three numbers. Here we will see the other expressions of A plus B plus C whole Square Formula or you can say other forms of (a + b + c)2 formula.
We can derive this formula (a + b + c)2 formula by just multiplying (a+b+c) by itself. so here we will see the expansion of A plus B plus C ka whole cube.
- (a + b + c)2 = (a + b + c)(a + b + c)
- (a + b + c)2 = a2 + ab + ac + ab + b2 + bc + ca + bc + c2
- (a + b + c)2 = a2 + b2 + c2 + 2ab + 2bc + 2ca
- (a + b + c)2 = a2 + b2 + c2 + 2(ab + bc + ca)
List of Some important Algebraic formula
- (x + y + z)2 = x2 + y2 + z2 + 2xy +2yz + 2xz
- (x + y – z)2 = x2 + y2 + z2 + 2xy – 2yz – 2xz
- (x – y + z)2 = x2 + y2 + z2 – 2xy – 2yz + 2xz
- (x – y – z)2 = x2 + y2 + z2 – 2xy + 2yz – 2xz
- x3 + y3 + z3 – 3xyz = (x + y + z) (x2 + y2 + z2 – xy – yz -xz)
- x3 + y3 = (x + y) (x2 – xy + y2)
- x3 – y3 = (x – y) (x2 + xy + y2)
- (a – b)3 = a3 – b3 – 3ab (a – b)
- (a + b)3 = a3 + b3 + 3ab (a + b)
- (a + b)2 = a2 + 2ab + b2
- (a – b)2 = a2 – 2ab + b2
- (a + b) (a – b) = a2 – b2
- (a + b)4 = a4 + 4a3b + 6a2b2 + 4ab3 + b4
- (a – b)4 = a4 – 4a3b + 6a2b2 – 4ab3 + b4
Solved examples using (a + b + c)2 formula
Now you can understand this a b c whole square (a+ b + c)2 = a2 + b2 + c2 + 2(ab + bc + ca) formula in detail by solving some good examples
Example 1: Find the value of the following expression a2 + b2 + c2 if a + b + c = 20 and ab + bc + ca = 20 using (a + b + c)2 algebraic identity.
Solution: In this question we have to find: a2 + b2 + c2 and what is given in the question a + b + c = 20 and ab + bc + ca = 2
Now we will solve above question by using the a b c whole square (a+ b + c)2 = a2 + b2 + c2 + 2(ab + bc + ca) formula or A plus B plus C whole square formula.
a2 + b2 + c2 = (a + b + c)2 – 2(ab + bc + ca)
[Note: substitute the value of a + b + c = 20 and ab + bc + ca = 2 already given in question]
a2 + b2 + c2 = (20)2 – 2(20) = 400 – 40 = 360
Answer: a2 + b2 + c2 = 360.
Example 2: Find the value of a2 + b2 + c2 if a + b + c = -3, 1/a + 1/b + 1/c = 3 and abc = 4 using (a + b + c)2 formula.
Solution: we have to find: a2 + b2 + c2 in the question, the following equations are given:
a + b + c = -3 suppose its equation (1)
1/a + 1/b + 1/c = 3 suppose its equation (2)
abc = 4 suppose its equation (3)
Now we will multiply equation (2) with equation (3),
(abc) x (1/a + 1/b + 1/c) = (4) x (3)
As a result we will get (bc + ca + ab) = 12 suppose its equation (4)
Now lets use (a+ b + c)2 = a2 + b2 + c2 + 2(ab + bc + ca) formula or A plus B plus C whole square formula,
Rewrite the formula as a2 + b2 + c2 = (a + b + c)2 – 2(ab + bc + ca) and substitute the values of (a+b+c) and (bc + ca + ab) from equation 1 and 4
a2 + b2 + c2 = (-3)2 – 2(12) = 9 – 24 = -15
Answer: a2 + b2 + c2 = -15.
FAQs on a b c whole square formula
A plus B plus C ka whole square formula is (a + b + c)2 = a2 + b2 + c2 + 2(ab + bc + ca) . Read about a b c whole square.
You can rewrite this (a + b + c)2 = a2 + b2 + c2 + 2(ab + bc + ca) as a2 + b2 + c2 = (a + b + c)2 – 2(ab + bc + ca). Read about a b c whole square.
(a + b + c)2 = a2 + b2 + c2 + 2(ab + bc + ca). Read about a b c whole square.
(a + b + c)2 = a2 + b2 + c2 + 2(ab + bc + ca)
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