\(a,=4x^2+4x+1\\ b,=9-12y+4y^2\\ c,=\dfrac{x^2}{4}-xy+y^2\\ d,=\dfrac{25}{4}-5x+x^2\\ e,=4x^2+32xy+64y^2\\ f,=9x^2-30xy+25y^2\)

a. (2x + 1)² 

= 4x² + 4x + 1

b. (3 - 2y)²

= 9 - 12y + 4y²

- Các câu còn lại bn dung CT: (A + B)² = A² + 2AB + B² và (A - B)² = A² - 2AB + B² để tính tiếp nha, phân số cũng đc tính.)

a. Ta có :

x²-9= (x-3)(x+3)

=> Mtc : (x-3)(x+3)

Nhân tử phụ 1 : (x-3)(x+3):(x-3)(x+3)=1

Nhân tử phụ 2 : (x-3)(x+3):(x+3)=x-3

Qui đồng:

x+15/x²-9= x+15/(x-3)(x+3)=(x-15).1/(x-3)(x+3).1=x-15/(x-3)(x+3)

2/x+3=2.(x-3)/(x+3)(x-3)=2(x-3)/(x-3)(x+3)

        x-15/(x-3)(x+3)       +      2(x-3)/(x-3)(x+3)

  =   (x-15)+2(x-3)/(x-3)(x+3)

  =    x-15+2/x+3 

  =  x-13/x+3

giúp mình nha mình cần gấp, cảm ơn mọi người trước

a) (2x+3)²

=4x^2+12x+9

b) (x-2/5)³

=x^3-1.2x^2+0.48x-0.064

c) (4x²+1)³

=(4x^2)^3+12x^4+12x^2+1

`a)A=x(x+y)-x(y-x)`

`=x^2+xy-xy+x^2`

`=2x^2`

Thay `x=-3`

`=>A=2.9=18`

`b)B=4x(2x+y)+2y(2x+y)-y(y+2x)`

`=8x^2+4xy+4xy+2y^2-y^2-2xy`

`=8x^2+y^2+6xy`

Thay `x=1/2,y=-3/4`

`=>B=8*1/4+9/16-9/4`

`=2+9/16-9/4`

`=9/16-1/4=5/16`

\(2x\left(x^2-7x-3\right)=2x^3-14x-6x\)

\(4xy^2\left(-2x^3+y^2-7xy\right)=-8x^4y^2+4xy^5-28x^2y^3\)

a: \(=\left(2x-y\right)\left(x+y+3x-y\right)+\left(2x-y\right)\)

\(=\left(2x-y\right)\left(4x+1\right)\)

b: \(=abc\left(b^2c-abc+bc^2-a\right)\)

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

a: \(\dfrac{20a^4b^5c^2}{\left(-5ab^2c\right)^2}\)

\(=\dfrac{20a^4b^5c^2}{25a^2b^4c^2}\)

\(=\dfrac{4}{5}a^2b\)

b: \(\dfrac{\left(-15x^2y^3\right)^7}{\left(15xy^3\right)^6}-\dfrac{32x^{18}y^5}{\left(-4x^5y\right)^2}\)

\(=\dfrac{-15^7\cdot x^{14}\cdot y^{21}}{15^6\cdot x^6\cdot y^{18}}-\dfrac{32x^{18}y^5}{16x^{10}y^2}\)

\(=-15x^8y^3-2x^8y^3\)

c: \(\dfrac{-\dfrac{1}{3}x^5y^2}{-2xy}-\dfrac{x^2+2x+1}{x+1}\)

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

Bài 3:

a: \(\frac{x}{x-3}+\frac{9-6x}{x^2-3x}\)

\(=\frac{x}{x-3}+\frac{-6x+9}{x\left(x-3\right)}\)

\(=\frac{x^2-6x+9}{x\left(x-3\right)}=\frac{\left(x-3\right)^2}{x\left(x-3\right)}=\frac{x-3}{x}\)

b: \(\frac{6x-3}{x}:\frac{4x^2-1}{3x^2}\)

\(=\frac{3\left(2x-1\right)}{x}\cdot\frac{3x^2}{\left(2x-1\right)\left(2x+1\right)}=\frac{3\cdot3x}{2x+1}=\frac{9x}{2x+1}\)

Bài 2:

a: \(\frac{x^3-x}{3x+3}\)

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

b: \(\frac{x^2+3xy}{x^2-9y^2}=\frac{x\left(x+3y\right)}{\left(x-3y\right)\left(x+3y\right)}=\frac{x}{x-3y}\)

Bài 1:

a: \(\frac{x^2-9}{2x+6}:\frac{3-x}{2}\)

\(=\frac{\left(x-3\right)\left(x+3\right)}{2\left(x+3\right)}\cdot\frac{2}{-\left(x-3\right)}=\frac{-2}{2}=-1\)

b: \(\frac{2x}{x-y}-\frac{2y}{x-y}=\frac{2x-2y}{x-y}=\frac{2\left(x-y\right)}{x-y}=2\)

c: \(\frac{x+15}{x^2-9}+\frac{2}{x+3}\)

\(=\frac{x+15}{\left(x-3\right)\left(x+3\right)}+\frac{2}{x+3}\)

\(=\frac{x+15+2\left(x-3\right)}{\left(x-3\right)\left(x+3\right)}=\frac{x+15+2x-6}{\left(x-3\right)\left(x+3\right)}=\frac{3x+9}{\left(x-3\right)\left(x+3\right)}\)

\(=\frac{3\left(x+3\right)}{\left(x-3\right)\left(x+3\right)}=\frac{3}{x-3}\)

d: \(\frac{x+y}{2x-2y}-\frac{x-y}{2x+2y}-\frac{y^2+x^2}{y^2-x^2}\)

\(=\frac{x+y}{2\left(x-y\right)}-\frac{x-y}{2\left(x+y\right)}+\frac{x^2+y^2}{\left(x-y\right)\left(x+y\right)}\)

\(=\frac{\left(x+y\right)^2-\left(x-y\right)^2+2\left(x^2+y^2\right)}{2\left(x-y\right)\left(x+y\right)}=\frac{x^2+2xy+y^2-x^2+2xy-y^2+2x^2+2y^2}{2\left(x-y\right)\left(x+y\right)}\)

\(=\frac{2x^2+4xy+2y^2}{2\left(x-y\right)\left(x+y\right)}=\frac{2\left(x^2+2xy+y^2\right)}{2\left(x-y\right)\left(x+y\right)}=\frac{\left(x+y\right)^2}{\left(x-y\right)\left(x+y\right)}=\frac{x+y}{x-y}\)

a: \(\left(19x^2-14x^3+9-20x+2x^4\right):\left(1+x^2-4x\right)\)

\(=\left(2x^4-14x^3+19x^2-20x+9\right):\left(x^2-4x+1\right)\)

\(=\left(2x^4-8x^3+2x^2-6x^3+24x^2-6x-7x^2+28x-7-42x+16\right)\) :\(\left(x^2-4x+1\right)\)

\(=2x^2-6x-7+\frac{-42x+16}{x^2-4x+1}\)

b: \(\left(3x^4-2x^3-2x^2+4x+8\right):\left(x^2-2\right)\)

\(=\left(3x^4-6x^2-2x^3+4x+4x^2-8+16\right):\left(x^2-2\right)\)

\(=3x^2-2x+4+\frac{16}{x^2-2}\)

c: \(\left(2x^3-26x-24\right):\left(x^2+4x+3\right)\)

\(=\left(2x^3+8x^2+6x-8x^2-32x-24\right):\left(x^2+4x+3\right)\)

=2x-8