Question

8(a+b)^3-27c^3 factorize​

Answer 1

GIVEN :

The polynomial expression is $8(a+b)^3-27c^3$

TO FIND :

The factors of the given polynomial expression by factorization.

SOLUTION :

Given that the polynomial expression is  $8(a+b)^3-27c^3$

Now simplifying the given polynomial expression.

$8(a+b)^3-27c^3$

$=2^3(a+b)^3-3^3c^3$

By using the property of exponent power rules is given by :

$a^m.b^m=(ab)^m$

$=(2(a+b))^3-(3c)^3$

By using the algebraic identity:

$a^3-b^3=(a-b)(a^2+ab+b^2)$

$=(2(a+b)-3c)((2(a+b))^2+(2(a+b))(3c)+(3c)^2)$

By using the property of exponent power rules is given by :

$a^m.b^m=(ab)^m$

$=(2(a+b)-3c)(2^2(a+b)^2+6c(a+b)+3^2c^2)$

$=(2(a+b)-3c)(4(a+b)^2+6c(a+b)+9c^2)$

$=(2(a+b)-3c)[(2(a+b))(2(a+b)+3c)+9c^2]$

∴ $8(a+b)^3-27c^3=(2(a+b)-3c)[(2(a+b))(2(a+b)+3c)+9c^2]$

∴ the simplified form of the given expression $8(a+b)^3-27c^3$ is $(2(a+b)-3c)[(2(a+b))(2(a+b)+3c)+9c^2]$

Answer 2

please make me as BRAINLIST