Thực hiện phép tính: a, (x+3)(x-3)-(x-2)(x+5) b, (2x^3-11x^2+6x-5):(2x^2-x+1) c, (x+1)(x^2-x+1)-(3+x)(9-3x+x^2) d, (2x+3)(4x^2-6x+9)-2(4x^3-1) e, (x^3-3x^2+3xy^2-y^3):(x^2-2xy+y^2)
Thực hiện phép tính: a, (x+3)(x-3)-(x-2)(x+5) b, (2x^3-11x^2+6x-5):(2x^2-x+1) c, (x+1)(x^2-x+1)-(3+x)(9-3x+x^2) d, (2x+3)(4x^2-6x+9)-2(4x^3-1)
By Kaylee
a, $(x+3)(x-3)-(x-2)(x+5)$
$=x^2-9-(x^2+5x-2x-10)$
$=x^2-9-x^2-3x+10$
$=1-3x$
b, $\dfrac{2x^3-11x^2+6x-5}{2x^2-x+1}$
$=\dfrac{x^3-10x^2-x^2+5x+x-5}{2x^2-x+1}$
$=\dfrac{x^2(x-5)-x(x-5)+(x-5)}{2x^2-x+1}$
$=\dfrac{(x-5)(x^2-x+1)}{2x^2-x+1}$
$=x-5$
c, $(x+1)(x^2-x+1)-(3+x)(9-3x+x^2)$
$=x^3+1-(27+x^3)$
$=x^3+1-27-x^3$
$=-26$
d, $(2x+3)(4x^2-6x+9)-2(4x^3-1)$
$=8x^3+27-8x^3+2$
$=29$
e, $\dfrac{x^3-3x^2y+3xy^2-y^3}{x^2-2xy+y^2}$
$=\dfrac{(x-y)^3}{(x-y)^2}$
$=x-y$