Factorize (A - B + C)2 + (B - C + A)2 + 2(A - B + C)(B - C + A) - Mathematics

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Answer in Brief

Factorize (a - b + c)2 + (b - c + a)2 + 2(a - b + c) (b - c + a)

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Solution

Let (a - b + c) = x and (b - c + a ) = y

= x2 + y2 + 2xy

Using identity a2  + b2  + 2ab = (a + b)2

= ( x + y )2

Now, substituting x and y

= (a - b + c + b - c + a)2

Cancelling -b, +b and +c, -c

= (2a )2

= 4a2

∴ (a - b + c)2 + (b - c + a)2 + 2(a - b + c)(b - c + a )  = 4a2

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Chapter 5: Factorisation of Algebraic Expressions - Exercise 5.1 [Page 9]

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RD Sharma Mathematics for Class 9
Chapter 5 Factorisation of Algebraic Expressions
Exercise 5.1 | Q 9 | Page 9

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