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Question
Factorise the following:
x3 + 8y3 + 6xy – 1
Sum
Solution
x3 + 8y3 + 6xy – 1 = – (– x3 – 8y3 – 6xy + 1)
= – (– x3 – 8y3 + 1 – 6xy)
= – [(– x)3 + (– 2y)3 + 1 – 3(x)(2y)(1)]
= – [– x – 2y + 1] [(– x)2 + (– 2y)2 + 12 – (– x)(– 2y) – (– 2y)(1) – (1)(– x)]
= (x + 2y – 1)(x2 + 4y2 + 1 – 2xy + 2y + x)
shaalaa.com
Factorisation using Identity a3 + b3 + c3 - 3abc = (a + b + c)(a2 + b2 + c2 - ab - bc - ca)
Is there an error in this question or solution?
Chapter 3: Algebra - Exercise 3.5 [Page 105]
