Question

Pls help me with question number 3

Have to factorise;

Answer 1

8p^3 + 12p^2/5 + 6p/25 + 1/25

8p^3 + 2.4p^2 + 0.24p + 0.04

8(p^3 + 0.3p^2 + 0.03p + 0.005)

8(p^3 + 0.3p^2 + 0.03p + 0.001- 0.001 + 0.005)

8(( p+ 0.1)^3 + 0.004)

8( ( p + 0.1)^3 + (2^(2/3)/10)^3)

now it is in form

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

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

so

a = p+0.1

b = (2^2/3)/10

put in above we get

8{p + 0.1 +2^(2/3)/10 } {(p+0.1)^2 - (p+0.1)(2^(2/3)/10 ) + 2^(4/3)}