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.
