Đáp án:
$1)\\a)14x^3−10x^2−2x\\ b)−x^3y−2x^2y^2+3xy\\ c)−4x^5y+6x^3y^2−10x^3y^2z\\ d)12x^{n+3}-8x^{n+2}\\ 2)\\ a)135\\ b)\dfrac{6}{5}\\ c)-26$
Giải thích các bước giải:
$1)\\ a)2x(7x^2-5x-1)\\ =14x^3−10x^2−2x\\ b)(x^2+2xy-3)(-xy)\\ =−x^3y−2x^2y^2+3xy\\ c)-2x^3y(2x^2-3y+5yz)\\ =−4x^5y+6x^3y^2−10x^3y^2z\\ d)\left(3x^{n+1}-2x^n\right).4x^2\\ =12x^{n+3}-8x^{n+2}\\ 3)\\ a)A=5x(4x^2-2x+1)-2x(10x^2-5x-2)\\ =20x^3−10x^2+5x-(20x^3−10x^2−4x)\\ =20x^3−10x^2+5x-20x^3+10x^2+4x\\ =9x\\ x=15; A=135\\ b)B=5x(x-4y)-4y(y-5x)\\ =5x^2-20xy-4y^2+20xy\\ =5x^2-4y^2\\ x=-\dfrac{1}{5};y=-\dfrac{1}{2}; B=5\left(-\dfrac{1}{5}\right)^2-4\left(-\dfrac{1}{2}\right)^2=-\dfrac{4}{5}\\ c)C=6xy(xy-y^2)-8x^2(x-y^2)+5y^2(x^2-xy)\\ =6x^2y^2-6xy^3-8x^3+8x^2y^2+5x^2y^2-5xy^3\\ =19x^2y^2-11xy^3-8x^3\\ x=\dfrac{1}{2};y=2;C=19.\left(\dfrac{1}{2}\right)^2.2^2-11.\dfrac{1}{2}.2^3-8.\left(\dfrac{1}{2}\right)^3=-26$
