Verify the following: (a2 – b2)(a2 + b2) + (b2 – c2)(b2 + c2) + (c2 – a2) + (c2 + a2) = 0

Verify the following:

(a² – b²)(a² + b²) + (b² – c²)(b² + c²) + (c² – a²) + (c² + a²) = 0

Sum

Taking L.H.S. = (a² – b²)(a² + b²) + (b² – c²)(b² + c²) + (c² – a²) + (c² + a²)

= (a⁴ – b⁴ + b⁴ – c⁴ + c⁴ – a⁴) ...[Using the identity, (a – b)(a + b) = a² – b²]

= 0

= R.H.S.

Hence verified.

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Chapter 7: Algebraic Expression, Identities and Factorisation - Exercise [Page 238]

Chapter 7 Algebraic Expression, Identities and Factorisation
Exercise | Q 113. (vii) | Page 238

Factorise : 16p⁴ – 1

Using the identity (a + b)(a – b) = a² – b², find the following product

(p + 2)(p – 2)

Using the identity (a + b)(a – b) = a² – b², find the following product

(1 + 3b)(3b – 1)

The pathway of a square paddy field has 5 m width and length of its side is 40 m. Find the total area of its pathway. (Note: Use suitable identity)

Using suitable identities, evaluate the following.

(729)² – (271)²