Đáp án:
$1)\\ a)8x^3+4x^2y+\dfrac{2}{3}xy^2+\dfrac{y^3}{27}\\ b)27x^3-\dfrac{27}{4}x^2y+\dfrac{9}{16}xy^2+\dfrac{y^3}{64}\\ c)\left(2x-\dfrac{y}{3}\right)\left(4x^2+\dfrac{2}{3}xy+\dfrac{y^2}{9}\right)\\ d)(x+2y)(x^2+2xy+4y^2)\\ 2)\\ a)(x+2y)^3\\ b)(5-3y)^3\\ c)(x-2)^3$
Giải thích các bước giải:
$1)\\ a)\left(2x+\dfrac{1}{3}y\right)^3\\ =\left(2x+\dfrac{y}{3}\right)^3\\ =(2x)^3+3.(2x)^2.\dfrac{y}{3}+3.2x.\left(\dfrac{y}{3}\right)^2+\left(\dfrac{y}{3}\right)^3\\ =8x^3+4x^2y+\dfrac{2}{3}xy^2+\dfrac{y^3}{27}\\ b)\left(3x-\dfrac{1}{4}y\right)^3\\ =\left(3x-\dfrac{y}{4}\right)^3\\ =(3x)^3-3.(3x)^2.\dfrac{y}{4}+3.3x.\left(\dfrac{y}{4}\right)^2-\left(\dfrac{y}{4}\right)^3\\ =27x^3-\dfrac{27}{4}x^2y+\dfrac{9}{16}xy^2+\dfrac{y^3}{64}\\ c)8x^3-\dfrac{1}{27}y^3\\ =(2x)^3-\dfrac{y^3}{27}\\ =(2x)^3-\left(\dfrac{y}{3}\right)^3\\ =\left(2x-\dfrac{y}{3}\right)\left((2x)^2+2x.\dfrac{y}{3}+\left(\dfrac{y}{3}\right)^2\right)\\ =\left(2x-\dfrac{y}{3}\right)\left(4x^2+\dfrac{2}{3}xy+\dfrac{y^2}{9}\right)\\ d)x^3+8y^3\\ =x^3+(2y)^3\\ =(x+2y)(x^2+x.2y+(2y)^2)\\ =(x+2y)(x^2+2xy+4y^2)\\ 2)\\ a)x^3+6x^2y+12xy^2+8y^3\\ =x^3+3.x^2.2y+3.x.(2y)^2+(2y)^3\\ =(x+2y)^3\\ b)125-225y+135y^2-27y^3\\ =125-3.25.3y+3.5.9y^2-27y^3\\ =5^3-3.5^2.3y+3.5.(3y)^2-(3y)^3\\ =(5-3y)^3\\ c)x^3-6x^2+12x-8\\ =x^3-3.x^2.2+3.x.2^2-2^3\\ =(x-2)^3$
