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The (a- b- c)2formula is used to lớn find the squareof the difference between the three numbers without actually calculating the whole square and in factorization.(a- b- c)2formula is one of the major algebraic identities.To derive the expansion of (a- b- c)2formula we just multiply(a - b - c) by itself lớn get(a - b - c)2. Let us learn more about the (a- b- c)2 formula along with solved examples.

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What Is(a- b- c)2 Formula?

We just read that by multiplying(a - b - c) by itself we can easily derive the(a - b - c)2formula. Let us see the expansion of(a- b- c)2formula.(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)

Let us see how lớn use the (a- b- c)2formulain the following section.



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Examples on(a- b- c)2 Formula

Let us take a look at a few examples to lớn better understand the formula of(a- b- c)2.

Example 1:Find the value of (a- b- c)2if a = 2,b = 4, và c = 3using(a - b - c)2formula.

Solution:

To find: (a- b- c)2Given that:a = 2, b = 4, c = 3Using the(a - b - c)2formula,(a- b- c)2= a2+ b2+ c2- 2ab + 2bc - 2ca(a- b- c)2= 22 + 42+ 32 - 2(2)(4) +2(4)(3) - 2(3)(2)(a- b- c)2= 4 + 16 + 9 - 16 + 24 - 12

Answer:(a- b- c)2= 25.

Example 2:Find the value of (a- b- c)2if a = 12,b = 4, và c = 5using(a - b - c)2formula.

Solution:

To find: (a- b- c)2Given that:a = 12, b = 4, c = 5Using the(a - b - c)2formula,(a- b- c)2= a2+ b2+ c2- 2ab + 2bc - 2ca(a- b- c)2= 122 + 42+ 52 - 2(12)(4) +2(4)(5) - 2(5)(12)(a- b- c)2= 144 + 16 + 25 - 96 + 40 - 120 = 9

Answer:(a- b- c)2= 9.

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Example 3:Find the value of a2+ b2+ c2if (ab - bc + ca) = 10 & (a - b - c) = trăng tròn using(a - b - c)2formula.

Solution:

To find: a2+ b2+ c2Given that:(ab-bc+ca) = 10 & (a - b - c) = 20Using the(a - b - c)2formula,(a- b- c)2= a2+ b2+ c2- 2(ab - bc + ca)(20)2= a2+ b2+ c2- 2(10)400 =a2+ b2+ c2- 20a2+ b2+ c2= 400 + 20 = 420

Answer:(a- b- c)2= 420.


FAQs on(a -b - c)2Formulas

What Is the Expansion of (a -b - c)2Formula?

(a -b - c)2formula is read as a minusb minus c whole square. Its expansion is expressed as(a- b- c)2= a2+ b2+ c2- 2ab + 2bc - 2ca.

What Is thea2- b2- c2Formula in Algebra?

The (a - b - c)2formula is one of the importantalgebraic identities. It is read as a minus b minusc whole square. The (a - b - c)2formula is expressed as(a- b- c)2= a2+ b2+ c2- 2ab + 2bc - 2ca.

How lớn Simplify Numbers Usingthe(a - b - c)2Formula?

Let us understand the use of the (a - b - c)2formula with the help of the following example.Example:Find the value of (2- 5- 3)2 using the (a - b - c)2formula.To find:(2- 5- 3)2Let us assume that a = 2and b = 5 và c = 3.We will substitute these in the formula of(a - b - c)2.(a- b- c)2= a2+ b2+ c2- 2ab + 2bc - 2ca= 22 + 52 + 32 - 2(2*5) + 2(5*3) - 2(3*2)= 4 + 25 + 9 - 2(10) + 2(15) - 2(6)Answer:(2- 5- 3)2= 36

How to Use the(a - b - c)2Formula Give Steps?

The following steps are followed while using(a - b - c)2formula.

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Firstlyobserve the pattern of the numbers whether the three numbers have ^2 as wholepower or not such as (a - b - c)2.Write down the formula of(a - b - c)2.(a- b- c)2= a2+ b2+ c2- 2ab + 2bc - 2ca.substitute the value ofa, b và c in the(a - b - c)2formula and simplify.