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Factroise (i) a^3+b^3+a+b (ii) a^3-b...

Factroise
`(i) a^3+b^3+a+b`
`(ii) a^3-b^3-a+b`

Text Solution

Verified by Experts

We have
`(i) a^3+b^3+a+b`
`=(a^3+b^3)+(a+b)`
`=(a+b)(a^2-ab+b^2)+(a+b)`
`=(a+b)xx{(a^2-ab+b^2)+1}`
`=(a+b)(a^2-ab+b^2+1)`.
`therefore (a^3+b^3+a+b)=(a+b)(a^2-ab+b^2+1)`.
`(ii) a^3-b^3-a+b`
`=(a^3-b^3)-(a-b)`
`=(a-b)(a^2+ab+b^2)-(a-b)`
`=(a-b)(a^2+ab+b^2 -1)`.
`therefore (a^3-b^3-a+b)=(a-b)(a^2+ab+b^2-1)`.
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