Đáp án:
Bài 1: Thực hiện phép tính:
$a) (xy-2)(xy+5)$
$=xy.xy+xy.5+(-2).xy+(-2).5$
$=x²y²+5xy-2xy-10$
$=x²y²+3xy-10$
$b) (13xy-2)(x³-3x+6)$
$=13xy.x³+13xy.(-3x)+13xy.6+(-2).x³+(-2).(-3x)+(-2).6$
$=13x^4y-39x²y+78xy-2x³+6x-12$
Bài 2: Thực hiện phép nhân đa thức với đa thức:
$a) (x+2x+1)(x+1)$
$=x.x+x.1+2x.x+2x.1+1.x+1.1$
$=x²+x+2x²+2x+x+2$
$=3x²+4x+2$
$b) (x³-x²+2x–1)(5–x)$
$=(−x+5)(x³−x²+2x−1)$
$=(-x).x³+(-x).(-x²)+(-x).2x+(-x).(-1)+5.x³+5.(-x²)+5.2x+5.(-1)$
$=-x^4+x³-2x²+x+5x³-5x²+10x-5$
$=-x^4+6x³-7x²+11x-5$
Từ câu b) t suy ra đc:
$(x–5)(x³-x²+2x–1)$
$=x.x³+x.(-x²)+x.2x+x.(-1)+(-5).x³+(-5).(-x²)+(-5).2x+(-5).(-1)$
$=x^4-x³+2x²-x-5x³+5x²-10x+5$
$=x^4-6x³-3x²+9x+5$
Bài 3: Thực hiện phép tính:
$a) (x–y)(x²+xy+y²)$
$=x.x²+x.xy+x.y²+(-y).x²+(-y).xy+(-y).y²$
$=x³+x²y+xy²-x²y-xy²-y³$
$=x³-y³$
$b) (x² - 2xy + y²)(x – y)$
$=x².x+x².(-y)+(-2xy).x+(-2xy).(-y)+y².x+y².(-y)$
$=x³-x²y-2x²y+2xy²+xy²+y³$
$=x³-3x²y+3xy²+y³$
$c) (x²y²-13xy+3y)(x–3y)$
$=x²y².x+x²y².(-3y)+(-13xy).x+(-13xy).(-3y)+3y.x+3y.(-3y)$
$=x³y²-3x²y³-13x²y+39xy³+3xy-9y²$
$d) (15x–1)(x²-5x+2)$
$=15x.x²+15x.(-5x)+15x.2+(-1).x²+(-1).(-5x)+(-1).2$
$=15x³-75x²+30x-x²+5x-2$
$=15x³-76x²+25x-2$
Chúc bn hc tốt🥰
@LinhSad