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Harder Special Products And Factors-Chapter 6- Class 8- Advance Math

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Exercise- 6
1. Factorize
(i) (b+c)(c+a)(a+b)+abc
Solution:
(b+c)(c+a)(a+b)+abc
= (b+c){c(a+b)+a(a+b)}+abc
= (b+c)(ac+bc++ab)+abc
= (b+c)(+ab+ac+bc)+abc
(b+c){+a(b+c)+bc}+abc
(b+c)+a(b+c)(b+c)+bc(b+c)+abc
= a(b+c){a+b+c}+bc{b+c+a}
= (a+b+c){a(b+c)+bc}
= (a+b+c)(ab+ac+bc)

(ii)  a(-)+b(-)+c(-)
Solution:
a(-)+b(-)+c(-)
= a(b+c)(b-c)+b-b+c-c
= a(b+c)(b-c)+b-c-b+c
= a(b+c)(b-c)-bc(b-c)-(b-c)
= (b-c){a(b+c)-bc-}
= (b-c)(ab+ac-bc-)
= (b-c)<(-+ab+ac-bc)
= (b-c){-a(a-b)+c(a-b)}
= (b-c)(a-b)(c-a)

(iii) (-)+(-)+(-)
Solution:
 (-)+(-)+(-)
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