Examples on (a + b – c)²
Example 1: Evaluate: (A + 5B – 2C)2.
Solution:
For (A + 5B – 2C)2
a = A, b = 5B and c = 2C,
Thus, using (a + b – c)2 = a2 + b2 + c2 + 2(ab – bc – ca)
(A + 5B – 2C)2 = (A)2 + (5B)2 + (2C)2 + 2(A)(5B) + 2(5B)(-2C) + 2(A)(-2C)
⇒ (A + 5B + 2C)2 = A2 + 25B2 + 4C2 + 10AB – 20BC – 4AC
Example 2: Find the value of (a + b – c)2 if a = 2, b = 2, and c = 4.
Solution:
(a + b – c)² = a2 + b2 + c2 + 2ab – 2bc – 2ca
= 22+22+42 + 2(2)(2)-2(2)(4)-2(4)(2)
= 4 + 4 + 16 + 8 – 16 – 16
= 16 + 16 – 16 – 16 = 0
Example 3: Find the value of (a + b – c)2 if a = 2, b = 3, and c = 5.
Solution:
(a + b – c)² = a2 + b2 + c2 + 2ab – 2bc – 2ca
= 22 + 32 + 52 + 2(2)(3) – 2(3)(5) – 2(5)(2)
= 4+9+25+12-30-20
= 50 – 50 = 0
a plus b minus c Whole Square
The expression (a+b−c)2 is a binomial expression. It is represented as (a + b – c)². The Square of a number is defined as the product of the number itself. Hence, the value of (a + b – c) is (a + b – c) x (a + b – c).
a plus b minus c Whole Square
In this article, we will learn what the value of a plus b minus c whole square or (a + b – c)², how to find its value how to apply it in problems, and its applications. Let’s start our learning on the topic (a + b – c)2.