Chapter P - Prerequisites: Fundamental Concepts of Algebra - Exercise Set P.4 - Page 61: 53

$8x^3+36x^2+54x+27$

$$(2x+3)^3$$ $$=(2x+3)(2x+3)(2x+3)$$ $$=(2x+3)[(2x\times 2x)+(2x\times 3)+(3\times 2x)+(3\times 3)]$$ $$=(2x+3)(4x^2+6x+6x+9)$$ $$=(2x+3)(4x^2+12x+9)$$ $$=(2x\times 4x^2)+(2x\times 12x)+(2x\times 9)+(3\times 4x^2)+(3\times 12x)+(3\times 9)$$ $$=8x^3+24x^2+18x+12x^2+36x+27$$ $$=8x^3+36x^2+54x+27$$