TL:

1)\(\left(y^2-6y+9\right)-\left(3-y\right)^2=\left(y-3\right)^2-\left(3-y\right)^2\) 

   \(=\left(y-3+3-y\right)\left(y-3-3+y\right)=0.\left(2y-6\right)=0\) 

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

  \(=\left(x-3+x\right)\left(x-3-x\right)+16=\left(2x-3\right).\left(-3\right)+16=-6x+9+16\)  

 \(=-6x+25\)

 hc tốt

\(1,\left(y^2-6x+9\right)-\left(3-y\right)^2\)

\(=\left(y-3\right)^2-\left(y-3\right)^2=0\)

\(2,\left(x-3\right)^2-\left(x-4\right)\left(x+4\right)\)

\(=x^2-6x+9-x^2+16=-6x+21\)

\(3...\)\(< ->1\)

A = x²(x + y) - y(x² - y) + 2002

A = x².x + x².y + (-y).x² + (-y)(-y) + 2002

A = x³ + x²y - x²y + y² + 2002

A = x³ + (x²y - x²y) + y² + 2002

A = x³ + y² + 2002 (1)

Thay x = 1, y = -1 vào (1), ta có:

A = x³ + y² + 2002 = 1³ + (-1)² + 2002

                               = 1 + 1 + 2002

                               = 2004

B làm tương tự

cam on bn nhieu nha

#)Giải :

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

\(\text{x3 - 19x - 30}=x^3+2x^2-4x-15x-30\)

\(=x^2\left(x+2\right)-2x\left(x+2\right)-15\left(x+2\right)\)

\(=\left(x^2-2x-15\right)\left(x+2\right)\)

\(=\left[x^2-5x+3x-15\right]\left(x+2\right)\)

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

\(=\left(x+3\right)\left(x-5\right)\left(x+2\right)\)

\(x^3-19x+30\)

\(=x^3-9x-10x+30\)

\(=x\left(x^2-9\right)-10\left(x-3\right)\)

\(=x\left(x-3\right)\left(x+3\right)-10\left(x-3\right)\)

\(=\left(x-3\right)\left(x^2+3x-10\right)\)

\(=\left(x-3\right)\left(x^2-2x+5x-10\right)\)

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

\(=\left(x-2\right)\left(x-3\right)\left(x+5\right)\)

\(x^3-7x-6=x^3-x-6x-6=x\left(x^2-1\right)-6\left(x-1\right)=x\left(x-1\right)\left(x+1\right)-6\left(x-1\right)\)

\(=\left(x-1\right)\left(x^2+x-6\right)=\left(x-1\right)\left(x^2+3x-2x-6\right)=\left(x-1\right)\left(x\left(x+3\right)-2\left(x+3\right)\right)\)

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

\(\left[\frac{2}{3x}-\frac{2}{x+1}\left(\frac{x+1}{3x}-x-1\right)\right]:\frac{x-1}{x}\)

\(=\left[\frac{2}{3x}-\frac{2\left(x+1\right)}{\left(x+1\right).3x}-\frac{2\left(-x-1\right)}{x+1}\right]:\frac{x-1}{x}\)

\(=\)\(\left[\frac{2}{3x}-\frac{2\left(x+1\right)}{\left(x+1\right).3x}+\frac{2\left(x+1\right)}{x+1}\right]:\frac{x-1}{x}\)

\(=\left[\frac{2}{3x}-\frac{2}{3x}+2\right]:\frac{x-1}{x}\)

\(=2.\frac{x}{x-1}=\frac{2x}{x-1}\)\(\left(đpcm\right)\)

P=x^2(b-c)+b^2(c-x)+c^2(x-b)
P=X^2(b-c)+b^2[-(b-c)-(x-b)]+c^2(x-b)
P=x^2(b-c)-b^2(b-c)-b^2(x-b)+c^2(x-b)
P=(x^2-b^2)(b-c)- (b^2-c^2)(x-b)
P=(x+b)(x-b)(b-c)-(b+c)(b-c)(x-b)
P=(x-b)(b-c)(x+b-b-c)
P=(x-b)(b-c)(x-c)