Home
Class 9
MATHS
Factorize: (2a+1)^3+\ (a-1)^3...

Factorize: `(2a+1)^3+\ (a-1)^3`

Text Solution

Verified by Experts

We have,`(2a+1)^3+(a-1)^3= {(2a+1)+(a-1)} {(2a + 1)^2-(2a + 1)(a−1)+(a−1)^2}`
`[ x^3 + y^3 = (x + y)(x^2 − xy + y^2)]`
= `(2a+1+a-1){(4a^2+4a+1)-(2a^2-2a+a-1)+(a^2-2a+1)}`
`[(x + y)^2 = x^2 + 2xy + y^2]`
= `3a(4a^2+4a+1-2a^2+a+1+a^2-2a+1)`
`=3a(3a^2+3a+3)`
`=9a(a^2+a+1)`
`:.(2a + 1)^3 + (a − 1)^3=9a(a^2 + a + 1)`
Promotional Banner

Topper's Solved these Questions

  • EXPONENTS OF REAL NUMBER

    RD SHARMA|Exercise All Questions|186 Videos

  • FACTORIZATION OF POLYNOMIAL

    RD SHARMA|Exercise All Questions|220 Videos

Similar Questions

Explore conceptually related problems

Factorize: (x+1)^(3)-(x-1)^(3)

Factorize: (x+1)^(3)+(x-1)^(3)

Factorize: 1-27a^(3)

Factorize a^3+1

Factorize: x^(3)y^(3)+1

Factorize :(x+1)^(3)( ii) (x+1)^(3)+(x-1)^(3)8(x+y)^(3)-27(x-y)^(3)

factorize (a) (3a-1)^(2)-6a+2

Factorize : a^(3) + b^(3) + 3ab -1

Factorize: a^(3)-(1)/(a^(3))-2a+(2)/(a)

Factorize (2x+(1)/(3))^2-(x-(1)/(2))^2 .