The a2+ b2+ c2formula is supplied to find the amount of squares of 3 numbers without actually calculating the squares.a2+ b2+ c2formula is among the significant algebraic identities.To have the expansion of a2+ b2+ c2formula advice the(a + b + c)2formula. Let united state learn more about the a2+ b2+ c2 formula along with solved examples.

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## What Isa^2 + b^2 + c^2 Formula?

We just read the by multiplying(a + b + c) by itself us can easily derive thea2+ b2+ c2formula. Let united state see the expansion ofa2+ b2+ c2formula.(a + b + c)2=(a + b + c)(a + b + c)(a + b + c)2= a2+ ab + ac + abdominal muscle + b2+ bc + ca + bc + c2(a + b + c)2= a2+ b2+ c2+ 2ab + 2bc + 2ca(a + b + c)2=a2+ b2+ c2+ 2ab + 2bc + 2ca

On individually 2ab + 2bc + 2ca from both political parties of the above formula, thea2+ b2+ c2formula is:

a2+ b2+ c2= (a + b + c)2- 2 (ab + bc + ca)

(or)

a2+ b2+ c2= (a + b + c)2- 2ab -2bc -2ca

a2+ b2+ c2=(a + b + c)2- 2(ab + bc + ca)

We can additionally expressa2+ b2+ c2formula as,

a2+ b2+ c2=(a -b -c)2 + 2ab + 2ac -2bc

Let united state see how to usage the a2+ b2+ c2formulain the adhering to section.

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## Examples ona2+ b2+ c2Formula

Let us take a look in ~ a couple of examples to far better understand the formula ofa2+ b2+ c2 .

Example 1:Find the worth ofa2+ b2+ c2if a + b + c = 10 and ab + bc + ca = -2.

Solution:

To find: a2+ b2+ c2Given that:a + b + c = 10ab + bc + ca = -2Using thea2+ b2+ c2formula,a2+ b2+ c2= (a + b + c)2- 2(ab +bc +ca)a2+ b2+ c2= (10)2- 2(-2) = 100 + 4 = 104

Answer:a2+ b2+ c2= 104.

Example 2:Findthe value ofa2+ b2+ c2if a + b + c = -3, 1/a + 1/b + 1/c = -2 and also abc = 3.

Solution:

To find:a2+ b2+ c2Given that:a + b + c = -3 ... (1)1/a + 1/b + 1/c = -2 ... (2)abc = 3 ... (3)Multiplying (2) and also (3),abc(1/a + 1/b + 1/c) = (3)(−2)bc + ca + ab = −6Using thea2+ b2+ c2formula,a2+ b2+ c2= (a + b + c)2- 2(ab +bc +ca)a2+ b2+ c2= (-3)2- 2(-6) = 9 +12= 21

Answer:a2+ b2+ c2= 21.

Example 3:Find the worth ofa2+ b2+ c2if a + b + c = 20 and abdominal + bc + ca = 100.

Solution:

To find: a2+ b2+ c2Given that:a + b + c = 20ab + bc + ca = 100Using thea2+ b2+ c2formula,a2+ b2+ c2= (a + b + c)2- 2(ab +bc +ca)a2+ b2+ c2= (20)2- 2(100) = 400 - 200 = 200

Answer:a2+ b2+ c2= 200.

## FAQs ~ above a2+ b2+ c2Formulas

### What Is the development of a2+ b2+ c2Formula?

a2+ b2+ c2formula is check out as a square add to b square add to c square. Its expansion is express asa2+ b2+ c2= (a + b + c)2- 2(ab +bc +ca).

### What Is thea^2+ b^2+ c^2Formula in Algebra?

The a2+ b2+ c2formula is just one of the importantalgebraic identities. That is read as a square to add b square add to c square. The a2+ b2+ c2formula is to express asa2+ b2+ c2= (a + b + c)2- 2(ab +bc +ca).

### How To simplify Numbers Usingthea2+ b2+ c2Formula?

Let us recognize the usage of the a2+ b2+ c2formula v the help of the adhering to example.Example:Find the value of (22+ 52 + 32)using the a2+ b2+ c2formula.To find:(22+ 52 + 32)Let us assume the a = 2and b = 5 and also c = 3.We will certainly substitute this in the formula of(a2+ b2 + c2).a2+ b2+ c2= (a + b + c)2- 2(ab +bc +ca)= (2 + 5 + 3)2 - 2(2×5 + 5×3 + 3×2)=100 - 62 = 38Answer:(22+ 52 + 32) = 38

### How To use the(a2+ b2 + c2)Formula offer Steps?

The following steps are adhered to while using(a2+ b2 + c2)formula.

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Firstlyobserve the pattern of the numbers even if it is the three numbers have ^2 as individual strength or not.Write down the formula of(a2+ b2 + c2)a2+ b2+ c2= (a + b + c)2- 2(ab +bc +ca)Substitute the worths of a, b and c in thea2+ b2+ c2formula and also simplify.