a: =3x^3-15x^2+21x

b: =-x^3+6x^2+5x-4x^2-24x-20

=-x^3+2x^2-19x-20

c: =9x^2+15x-3x-5-7x^2-14

=2x^2+12x-19

d: =10x^2-4x+2/3

a: \(=\dfrac{5}{2x^2y}+\dfrac{2}{3xy}-\dfrac{y}{x^3}\)

\(=\dfrac{5\cdot3\cdot x}{6x^3y}+\dfrac{2\cdot2\cdot x^2}{6x^3y}-\dfrac{6y^2}{6x^3y}\)

\(=\dfrac{15x+4x^2-6y^2}{6x^3y}\)

b: \(=\dfrac{2x-7+3x+5}{10x-4}=\dfrac{5x-2}{10x-4}=\dfrac{1}{2}\)

c: \(=\dfrac{x^4-1-x^4+3x^2}{x^2-1}=\dfrac{3x^2-1}{x^2-1}\)

ĐKXĐ: \(x\notin\left\{-2;\dfrac{1}{2}\right\}\)

\(\dfrac{1}{x+2}+\dfrac{5}{2x^2+3x-2}\)

\(=\dfrac{1}{x+2}+\dfrac{5}{\left(x+2\right)\left(2x-1\right)}\)

\(=\dfrac{2x-1+5}{\left(x+2\right)\left(2x-1\right)}=\dfrac{2x+4}{\left(x+2\right)\left(2x-1\right)}\)

\(=\dfrac{2\left(x+2\right)}{\left(x+2\right)\left(2x-1\right)}=\dfrac{2}{2x-1}\)

\(\dfrac{1}{x+2}+\dfrac{5}{2x^2+3x-2}\)

\(=\dfrac{1}{x+2}+\dfrac{5}{2x^2+4x-x-2}\)

\(=\dfrac{1}{x+2}+\dfrac{5}{\left(2x^2+4x\right)-\left(x+2\right)}\)

\(=\dfrac{1}{x+2}+\dfrac{5}{2x\left(x+2\right)-\left(x+2\right)}\)

\(=\dfrac{1}{x+2}+\dfrac{5}{\left(x+2\right)\left(2x-1\right)}\)   (1)

ĐKXĐ: \(x\ne2;x\ne\dfrac{1}{2}\)

(1) \(=\dfrac{2x-1}{\left(x+2\right)\left(2x-1\right)}+\dfrac{5}{\left(x+2\right)\left(2x-1\right)}\)

\(=\dfrac{2x-1+5}{\left(x+2\right)\left(2x-1\right)}\)

\(=\dfrac{2x+4}{\left(x+2\right)\left(2x-1\right)}\)

\(=\dfrac{2\left(x+2\right)}{\left(x+2\right)\left(2x-1\right)}\)

\(=\dfrac{2}{2x-1}\)

a: \(=2x^2-4x-6x+12-2x^2+10x=12\)

a/\(\left(x-1\right)\left(x^5+x^4+x^3+x^2+x+1\right).\)

\(=\left(x-1\right)\left[\left(x^5+x^4+x^3\right)+\left(x^2+x+1\right)\right]\)

\(=\left(x-1\right)\left[x^3\left(x^2+x+1\right)+\left(x^2+x+1\right)\right]\)

\(=\left(x-1\right)\left(x^2+x+1\right)\left(x^3+1\right)\)

\(=\left(x-1\right)\left(x^2+x+1\right)\left(x+1\right)\left(x^2-x+1\right)\)

\(=\left(x-1\right)\left(x+1\right)\left(x^2-x+1\right)\left(x^2+x+1\right)\)

\(=\left(x^2-1\right)\left(x^2-x+1\right)\left(x^2+x+1\right)\)

Câu b/ quên làm ạ :> Bù nè

b/ \(2\left(3x-1\right)\left(2x+5\right)-\left(4x-1\right)\left(3x-2\right)\)

\(=2\left(6x^2+15x-2x-5\right)-\left(12x^2-8x-3x+2\right)\)

\(=2\left(6x^2+13x-5\right)-\left(12x^2-11x+2\right)\)

\(=12x^2+26x-10-\left(12x^2-11x+2\right)\)

\(=12x^2+26x-10-12x^2+11x-2\)

\(=37x-12\)

thanks ah

\(3x\left(4x-3\right)-\left(2x-1\right)\left(6x+5\right)\\ =12x^2-9x-\left(12x^2+10x-6x-5\right)\)

\(=12x^2-9x-\left(12x^2+4x-5\right)\\ =5-13x\)

\(3x\left(4x-3\right)-\left(2x-1\right)\left(6x+5\right)\)

\(=12x^2-9x-12x^2-10x+6x+5\)

\(=-13x+5\)

Answer:

\(3x^2.\left(2x^3-x+5\right)\)

\(=3x^2.2x^3+3x^2.(-x)+3x^2.5\)

\(=6x^5-3x^3+15x^2\)

\((4xy+3y-5x).x^2y\)

\(=4xy.x^2y+3y.x^2y-5x.x^2y\)

\(=4x^3+3x^2y^2-5x^3y\)

a) = 8x-6x-20+15x-15-6x+55-22x-30x+75

b)3x³+5x²-6x²+10x+9x-15-2x³+7x²+2x²+7x-2x-7

bạn chỉ cần chép lại đầu bài rồi ghi kết quả này vào là xong nhá bởi vì đây là nhân đa thức với đa thức mà

a) (2x-5)(4-3x)-(3x+11)(5-2x)-15(2x-5)

  =(2x-5)(4-3x)+(3x+11)(2x-5)-15(2x-5)

  =(2x-5)[(4-3x)+(3x+11)-15]

  =(2x-5)(4-3x+3x+11-15)

  = 2x-5

a: \(=\dfrac{2x^4+x^3-5x^2-3x-3}{x^2-3}\)

\(=\dfrac{2x^4-6x^2+x^3-3x+x^2-3}{x^2-3}\)

\(=2x^2+x+1\)

b: \(=\dfrac{x^5+x^2+x^3+1}{x^3+1}=x^2+1\)

c: \(=\dfrac{2x^3-x^2-x+6x^2-3x-3+2x+6}{2x^2-x-1}\)

\(=x+3+\dfrac{2x+6}{2x^2-x-1}\)

d: \(=\dfrac{3x^4-8x^3-10x^2+8x-5}{3x^2-2x+1}\)

\(=\dfrac{3x^4-2x^3+x^2-6x^3+4x^2-2x-15x^2+10x-5}{3x^2-2x+1}\)

\(=x^2-2x-5\)

Lời giải:

a.

$2x(3x^2-4x+2)=2x.3x^2-2x.4x+2x.2$

$=6x^3-8x^2+4x$

b.

$2x(3x+5)-3(2x^2-2x+3)=2x.3x+2x.5-(3.2x^2-3.2x+3.3)$

$=6x^2+10x-6x^2+6x-9=16x-9$