## What is the formula of A plus B plus C whole Square (a + b + c)^{2}

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

### List of Some important Algebraic formula

- (x + y + z)
^{2}= x^{2}+ y^{2}+ z^{2}+ 2xy +2yz + 2xz - (x + y – z)
^{2}= x^{2}+ y^{2}+ z^{2}+ 2xy – 2yz – 2xz - (x – y + z)
^{2}= x^{2}+ y^{2}+ z^{2}– 2xy – 2yz + 2xz - (x – y – z)
^{2}= x^{2}+ y^{2}+ z^{2}– 2xy + 2yz – 2xz - x
^{3}+ y^{3}+ z^{3}– 3xyz = (x + y + z) (x^{2}+ y^{2}+ z^{2}– xy – yz -xz) - x
^{3}+ y^{3}= (x + y) (x^{2 }– xy + y^{2}) - x
^{3}– y^{3}= (x – y) (x^{2 }+ xy + y^{2}) - (a – b)
^{3}= a^{3}– b^{3}– 3ab (a – b) - (a + b)
^{3}= a^{3}+ b^{3}+ 3ab (a + b) - (a + b)
^{2}= a^{2}+ 2ab + b^{2} - (a – b)
^{2}= a^{2}– 2ab + b^{2} - (a + b) (a – b) = a
^{2}– b^{2} - (a + b)
^{4}= a^{4}+ 4a^{3}b + 6a^{2}b^{2}+ 4ab^{3}+ b^{4} - (a – b)
^{4}= a^{4}– 4a^{3}b + 6a^{2}b^{2}– 4ab^{3}+ b^{4}

### Solved examples using (a + b + c)^{2} formula

Now you can understand this a b c whole square (a+ b + c)^{2 }= a^{2} + b^{2} + c^{2 } + 2(ab + bc + ca) formula in detail by solving some good examples

**Example 1: **Find the value of the following expression a^{2} + b^{2} + c^{2} 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: a^{2} + b^{2} + c^{2} 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 }= a^{2} + b^{2} + c^{2 } + 2(ab + bc + ca) formula or A plus B plus C whole square formula.

a^{2} + b^{2} + c^{2} = (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]

a^{2} + b^{2} + c^{2} = (20)^{2} – 2(20) = 400 – 40 = 360

**Answer:** a^{2} + b^{2} + c^{2} = 360.

**Example 2: **Find the value of a^{2} + b^{2} + c^{2} 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: a^{2} + b^{2} + c^{2} 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 }= a^{2} + b^{2} + c^{2 } + 2(ab + bc + ca) formula or A plus B plus C whole square formula,

Rewrite the formula as a^{2} + b^{2} + c^{2} = (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

a^{2} + b^{2} + c^{2} = (-3)^{2} – 2(12) = 9 – 24 = -15

**Answer:** a^{2} + b^{2} + c^{2} = -15.

#### FAQs on a b c whole square formula

**What Is the Expansion of (a + b + c)**

^{2}Formula?A plus B plus C ka whole square formula is (a + b + c)^{2} = a^{2} + b^{2} + c^{2} + 2(ab + bc + ca) . Read about a b c whole square.

**What Is the a**

^{2}+ b^{2}+ c^{2}Formula in Algebra?You can rewrite this (a + b + c)^{2} = a^{2} + b^{2} + c^{2} + 2(ab + bc + ca) as a^{2} + b^{2} + c^{2} = (a + b + c)^{2} – 2(ab + bc + ca). Read about a b c whole square.

**What is the formula for a b c whole square?**

(a + b + c)^{2} = a^{2} + b^{2} + c^{2} + 2(ab + bc + ca). Read about a b c whole square.

**How do you solve an ABC whole square?**

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

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