InterviewSolution
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InterviewSolution
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Factroise `(i) a^3-2sqrt(2)b^3` `(ii)1-64a^3` `(iii) 8a^3-27b^3` |
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Answer» We have `(i) (a^3-2sqrt(2)b^3)` `=(a)^3-(sqrt(2)b)^3` `=(a-sqrt(2)b)xx{a^2+(axx sqrt(2)b)+(sqrt(2)b)^2}` ` =(a-sqrt(2)b(a^2+sqrt(2)ab+2b^2)` `therefore (a^3-2sqrt(2)b^3)=(a-sqrt(2)b)(a^2+sqrt(2)ab 2b^2)`. `(ii) (1-64a^3)` `=(1)^3-(4a)^3` `=(1-4a)xx{1^2+(1xx4a)+(4a)^2} " " [because x^3-y^3=(x-y)(x^2+xy+y^2)]` `=(1-4a)(1+4a+16a^2)` `therefore (1-64a^3)=(1-4a)(1+4a+16a^2)` `(iii) (8a^3-27b^3)` `=(2a)^3-(3b)^3` `=(2a-3b)xx(4a^2+6ab+9b^2)` `therefore (8a^3-27b^3)=(2a-3b)(4a^2+6ab+9b^2)`. |
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