# Pythagorean theorem calculator

The a2+ b2+ c2formula is used lớn find the sum of squares of three numbers without actually calculating the squares.a2+ b2+ c2formula is one of the major algebraic identities.To derive the expansion of a2+ b2+ c2formula evaluate the(a + b + c)2formula. Let us learn more about the a2+ b2+ c2 formula along with solved examples.

Bạn đang xem: Pythagorean theorem calculator ## What Isa^2 + b^2 + c^2 Formula?

We just read that by multiplying(a + b + c) by itself we can easily derive thea2+ b2+ c2formula. Let us see the expansion ofa2+ b2+ c2formula.(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+ 2ab + 2bc + 2ca

On subtracting 2ab + 2bc + 2ca from both sides 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 also expressa2+ b2+ c2formula as,

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

Let us see how lớn use the a2+ b2+ c2formulain the following section.

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## Examples ona2+ b2+ c2Formula

Let us take a look at a few examples lớn better understand the formula ofa2+ b2+ c2 .

Example 1:Find the value ofa2+ b2+ c2if a + b + c = 10 & 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

Example 2:Findthe value ofa2+ b2+ c2if a + b + c = -3, 1/a + 1/b + 1/c = -2 và 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 (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

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Example 3:Find the value ofa2+ b2+ c2if a + b + c = 20 and ab + 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

## FAQs on a2+ b2+ c2Formulas

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

a2+ b2+ c2formula is read as a square plus b square plus c square. Its expansion is expressed 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 one of the importantalgebraic identities. It is read as a square plus b square plus c square. Its a2+ b2+ c2formula is expressed asa2+ b2+ c2= (a + b + c)2- 2(ab +bc +ca).

### How khổng lồ Simplify Numbers Usingthea2+ b2+ c2Formula?

Let us understand the use of the a2+ b2+ c2formula with the help of the following example.Example:Find the value of (22+ 52 + 32)using the a2+ b2+ c2formula.To find:(22+ 52 + 32)Let us assume that a = 2and b = 5 & c = 3.We will substitute these 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 lớn Use the(a2+ b2 + c2)Formula Give Steps?

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

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Firstlyobserve the pattern of the numbers whether the three numbers have ^2 as individual power nguồn or not.Write down the formula of(a2+ b2 + c2)a2+ b2+ c2= (a + b + c)2- 2(ab +bc +ca)Substitute the values of a, b and c in thea2+ b2+ c2formula and simplify.