Statement Expand the following expressions: (a) 12(x3−54)12\left(\dfrac{x}{3} - \dfrac{5}{4}\right)12(3x−45); (b) x2(3−4x)x^2(3 - 4x)x2(3−4x); (c) 4x(x2+2x+14x)4x\left(\dfrac{x}{2} + \dfrac{2}{x} + \dfrac{1}{4x}\right)4x(2x+x2+4x1). Solution Apply the distributive property. (a) 12⋅x3−12⋅54=4x−15.12\cdot\dfrac{x}{3} - 12\cdot\dfrac{5}{4} = 4x - 15.12⋅3x−12⋅45=4x−15. (b) x2⋅3−x2⋅4x=3x2−4x3.x^2\cdot 3 - x^2\cdot 4x = 3x^2 - 4x^3.x2⋅3−x2⋅4x=3x2−4x3. (c) 4x⋅x2+4x⋅2x+4x⋅14x=2x2+8+1=2x2+9.4x\cdot\dfrac{x}{2} + 4x\cdot\dfrac{2}{x} + 4x\cdot\dfrac{1}{4x} = 2x^2 + 8 + 1 = 2x^2 + 9.4x⋅2x+4x⋅x2+4x⋅4x1=2x2+8+1=2x2+9. 4x−15 ;3x2−4x3 ;2x2+9\boxed{4x - 15 \ ;\quad 3x^2 - 4x^3 \ ;\quad 2x^2 + 9}4x−15 ;3x2−4x3 ;2x2+9