Bài 1:

Bài 1:

a) \((x-5)(3x+3)-3x(x-3)+3x+7\)

\(=3(x-5)(x+1)-3x(x-3)+3x+7\)

\(=3(x^2+x-5x-5)-(3x^2-9x)+3x+7\)

\(=3(x^2-4x-5)-(3x^2-9x)+3x+7\)

\(=-8\)

b) \((x-3)(x^2+3x+9)-(54+x^3)\)

\(=(x-3)(x^2-3.x+3^2)-(54+x^3)\)

\(=x^3-3^3-(54+x^3)=-81\)

c) Sửa đề:

\((3x+y)(9x^2-3xy+y^2)-(3x-y)(9x^2+3xy+y^2)\)

\(=(3x+y)[(3x)^2-3x.y+y^2]-(3x-y)[(3x)^2+3x.y+y^2]\)

\(=(3x)^3+y^3-[(3x)^3-y^3]\)

\(=2y^3\)

Câu 2:

\(a)14x^2y^2-21xy^2+28x^2y\)

\(=7xy(2xy-3y+4x)\)

b) \((x+y)^2-4x^2\)\(=(x+y)^2-(2x)^2=(x+y-2x)(x+y+2x)\)

\(=(y-x)(3x+y)\)

c) \(2x^2-2xy-5x+5y\)

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

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

d) \(2xy-x^2-y^2+16\)

\(=16-(x^2+y^2-2xy)=4^2-(x-y)^2\)

\(=[4-(x-y)][4+(x-y)]=(4-x+y)(4+x-y)\)

Bài 3:
a)

\(x^2(x+1)+2x(x+1)=0\)

\(\Leftrightarrow (x+1)(x^2+2x)=0\)

\(\Leftrightarrow (x+1)x(x+2)=0\)

\(\Rightarrow \left[\begin{matrix} x+1=0\\ x=0\\ x+2=0\end{matrix}\right.\Rightarrow \left[\begin{matrix} x=-1\\ x=0\\ x=-2\end{matrix}\right.\)

b)

\(x(3x-2)-5(2-3x)=0\)

\(\Leftrightarrow x(3x-2)+5(3x-2)=0\)

\(\Leftrightarrow (3x-2)(x+5)=0\)

\(\Rightarrow \left[\begin{matrix} 3x-2=0\\ x+5=0\end{matrix}\right.\Rightarrow \left[\begin{matrix} x=\frac{2}{3}\\ x=-5\end{matrix}\right.\)

c)

\(16-25x^2=0\)

\(\Leftrightarrow 4^2-(5x)^2=0\)

\(\Leftrightarrow (4-5x)(4+5x)=0\)

\(\Rightarrow \left[\begin{matrix} 4-5x=0\\ 4+5x=0\end{matrix}\right.\Rightarrow \left[\begin{matrix} x=\frac{4}{5}\\ x=-\frac{4}{5}\end{matrix}\right.\)

a: \(=x^2+2xy+y^2+x^2-2xy+y^2=2x^2+2y^2\)

b: \(=\left(x+y+x-y\right)^2=\left(2x\right)^2=4x^2\)

d: \(=9x^2+6x+1-9x^2+6x-1=12x\)

a: \(=x^2+2xy+y^2+x^2-2xy+y^2=2x^2+2y^2\)

e: \(=x^3+1-x^3+1=2\)

Bài 2: 

a: \(A=\left(x+1\right)^3+5=20^3+5=8005\)

b: \(B=\left(x-1\right)^3+1=10^3+1=1001\)

Bài 2 :

Câu a : \(y\left(y^3+y^2-y-2\right)-\left(y^2-2\right)\left(y^2+y+1\right)\)

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

\(=2\) \(\Rightarrow\) ko phụ thuộc vào biến .

Câu b : \(\left(2x+3\right)\left(4x^2-6x+9\right)-2\left(4x^3-1\right)\)

\(=8x^3-12x^2+18x+12x^2-18x+27-8x^3+2\)

\(=29\Rightarrow\) ko thuộc vào biến

Câu c : \(3x\left(x+5\right)-\left(3x+18\right)\left(x-1\right)\)

\(=3x^2+15x-3x^2+3x-18x+18\)

\(=18\) \(\Rightarrow\) ko thuộc vào biến

Câu d : \(\left(2x+6\right)\left(4x^2-12x+36\right)-8x^3+5\)

\(=8x^3-24x^2+72x+24x^2-72x+216-8x^3+5\)

\(=221\) \(\Rightarrow\) không thuộc vào biến

câu 1) a) \(\left(x^2+2xy+y^2\right)\left(x+y\right)=\left(x+y\right)^2\left(x+y\right)=\left(x+y\right)^3\)

b) \(y\left(y^3+y^2-3y-2\right)+\left(y^2-2\right)\left(y^2+y-1\right)\)

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

\(=2y^4+2y^3-6y^2-4y+2=2y\left(y^3+y^2-3y-2\right)+2\)

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

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

c) \(6x^2-\left(2x+5\right)\left(3x-2\right)=6x^2-\left(6x^2-4x+15x-10\right)\)

\(\Leftrightarrow6x^2-6x^2+4x-15x+10=-11x+10\)

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

\(\)\(=6x^2+2x-3x-1+9x-6x^2+12-8x=11\)

e) \(\left(3x-5\right)\left(7-5x\right)-\left(5x+2\right)\left(2-3x\right)\)

\(=21x-15x^2-35+25x-\left(10x-15x^2+4-6x\right)\)

\(21x-15x^2-35+25x-10x+15x^2-4+6x=42x-39\)

a)(x2 – 2xy + y2)(x – y)

   = (x2 – 2xy + y2).x + (x2 – 2xy + y2).(–y)

   = x2.x + (–2xy).x + y2.x + x2.(–y) + (–2xy).(–y) + y2.(–y)

  = x3 – 2x2y + xy2 – x2y + 2xy2 – y3

   = x3 – (2x2y + x2y) + (xy2 + 2xy2) – y3

   = x3 – 3x2y + 3xy2 – y3.

c)6x^2-(2x+5) (3x-2)

6x^2-(6X²-4x+15x-10)

6x²-6x²+4x-15x+10

-11x+10

d)(2x-1)(3x+1)+(3x+4)(3-2x)

(=)6x2-3x+2x-1+6x-6x2+12-8x

  (=)-4x+11