(a + b - c)^2 Formula
The (a + b - c)2 formula is used to calculate the squares of three numbers with different operations. a plus b minus c Whole Square Formula is one of the major algebraic identities and can be applied in factorization. To derive the expansion of (a + b - c)2 formula we just multiply (a + b - c) by itself to get (a + b - c)2. Let us learn more about the (a + b - c)2 formula along with solved examples.
What Is (a + b - c)2 Formula?
We just read that by multiplying (a + b - c) by itself we can easily derive the A plus B minus C Whole Square Formula. Let us see the expansion of (a + b - c)2 formula.
(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 to use the (a + b - c)2 formula in the following section.
Examples on (a + b - c)2 Formula
Let us take a look at a few examples to better understand the formula of (a + b - c)2.
Example 1: Find the value of (a + b - c)2 if a = 2, b = 4, and c = 3 using A plus B minus C Whole Square Formula.
Solution:
To find: (a + b - c)2
Given that:
a = 2, b = 4, c = 3
Using the (a + b - c)2 formula,
(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 = 9.
Example 2: Find the value of (a + b - c)2 if a = 12, b = 4, and c = 5 using (a + b - c)2 formula.
Solution:
To find: (a + b - c)2
Given that:
a = 12, b = 4, c = 5
Using the (a + b - c)2 formula,
(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 = 121
Answer: (a + b - c)2 = 121.
Example 3: Find the value of a2 + b2 + c2 if (ab - bc - ca) = 10 and (a + b - c) = 20 using (a + b - c)2 formula.
Solution:
To find: a2 + b2 + c2
Given that:
(ab-bc-ca) = 10 and (a + b - c) = 20
Using the (a + b - c)2 formula,
(a + b - c)2 = a2 + b2 + c2 + 2(ab - bc - ca)
(20)2 = a2 + b2 + c2 + 2(10)
400 = a2 + b2 + c2 + 20
a2 + b2 + c2 = 400 - 20 = 380
Answer: a2 + b2 + c2 = 380.
FAQs on (a + b - c)2 Formulas
What Is the Expansion of (a + b - c)2 Formula?
(a + b - c)2 formula is read as a plus b minus c whole square. Its expansion is expressed as (a + b - c)2 = a2 + b2 + c2 + 2(ab - bc - ca).
What Is the (a + b - c)2 Formula in Algebra?
The (a + b - c)2 formula is one of the important algebraic identities. It is read as a plus b minus c whole square. The (a + b - c)2 formula is expressed as (a + b - c)2 = a2 + b2 + c2 + 2(ab - bc - ca).
How To Simplify Numbers Using the (a + b - c)2 Formula?
Let us understand the use of the (a + b - c)2 formula with the help of the following example.
Example: Find the value of (2 + 5 - 3)2 using the (a + b - c)2 formula.
To find: (2 + 5 - 3)2
Let us assume that a = 2 and b = 5 and c = 3.
We will substitute these in the formula of (a + b - c)2.
(a + b - c)2 = a2 + b2 + c2 + 2(ab - bc - ca)
= 22 + 52 + 32 + 2[(2*5) - (5*3) - (3*2)]
= 4 + 25 + 9 + 2[(10) - (15) - (6)]
= 4 + 25 + 9 + 2[-11]
Answer: (2 + 5 - 3)2 = 16
How To Use the A plus B minus C Whole Square Formula Give Steps?
The following steps are followed while using (a + b - c)2 formula.
- Firstly observe the pattern of the numbers whether the three numbers have ^2 as whole power or not, such as (a + b - c)2.
- Write down the formula of (a + b - c)2.
- (a + b - c)2 = a2 + b2 + c2 + 2(ab - bc - ca)
- Substitute the values of a, b, and c in the (a + b - c)2 formula and simplify.
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