Chapter P - Prerequisites: Fundamental Concepts of Algebra - Exercise Set P.4 - Page 61: 54

$27x^3+108x^2+144x+64$

$$(3x+4)^3$$ $$=(3x+4)(3x+4)(3x+4)$$ $$=(3x+4)[(3x\times 3x)+(3x\times 4)+(4\times 3x)+(4\times 4)]$$ $$=(3x+4)(9x^2+12x+12x+16)$$ $$=(3x+4)(9x^2+24x+16)$$ $$=(3x\times 9x^2)+(3x\times 24x)+(3x\times 16)+(4\times 9x^2)+(4\times 24x)+(4\times 16)$$ $$=27x^3+72x^2+48x+36x^2+96x+64$$ $$=27x^3+108x^2+144x+64$$