Factroise `(i) 1+64x^3` `(ii) 27x^3+125y^3` `(iii) (x+1)^3+(x-1)^3`

1.	Factroise `(i) 1+64x^3` `(ii) 27x^3+125y^3` `(iii) (x+1)^3+(x-1)^3`
Answer» We have `(i) 1+64x^3` `=(1)^3+(4x)^3` `=(1+4x)(1-4x+16x^2)` `(ii) 27x^3+125y^3` `=(3x)^3+(5y)^3` `=(3x+5y)(9x^2-15xy+25y^2)` (iii) Putting `(x+1)=a and (x-1)=b`, we get `(x+1)^3+(x-1)^3` `=(a^3+b^3)` ` =(a+b)(a^2-ab+b^2)` ` ={(x+1)+(x-1)}xx {(x+1)^2-(x+1)(x-1)+(x-1)^2}` ` =2xxx{(x^2+2x+1)-(x^2-1)+(x^2-2x+1)}` ` =2xx(x^2+2x+1-x^2+1+x^2-2x+1)=2x(x^2+3)`.

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