Question

015 Factorise
(1) 27a3+8
(ii) 8x3- (2x – 3y)3​

Answer 1

Answer:

(1). 27a^3+8

= (3a)^3+(2)^3

=(3a+2) {9a^2-6a+4)

The above line is written using the formula for (a)^3+(b)^3= (a+b) ( a^2-ab+b^2).

(2). 8x^3 - (2x-3y)^3

= (2x)^3-(2x-3y)^3

= (2x-2x+3y) {4x^2+2x(2x-3y)+(2x-3y)^2}

= 3y {4x^2+4x^2-6xy+4x^2-12xy+9y^2}

= 3y(12x^2-18xy+9y^2)

=36x^2y-54xy^2+27y^3