\(A = 2(x^6 + y^6) - 3(x^4 + y^4)\)

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

\(A = 2(x^2 + y^2)[(x^2 + y^2)^2 - 3x^2y^2] - 3[(x^2 + y^2)^2 - 2x^2y^2]\) (1)

thay \(x^2 + y^2 = 1\) vào (1) ta được:

\(A = 2 \cdot 1 \cdot [1^2 - 3x^2y^2] - 3[1^2 - 2x^2y^2]\)

\(A = 2(1 - 3x^2y^2) - 3(1 - 2x^2y^2)\)

\(A=2-6x^2y^2-3+6x^2y^2=-1\)

vậy A không phục thuộc vào x, y

a. \(3x(x-7) + 2xy - 14y\)

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

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

b. \(6x^2 - 12x + 6\)

\(= 6(x^2 - 2x + 1)\)

\(= 6(x-1)^2\)

c. \(9(2x-5)^2 + 15x - 6x^2\)

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

\(= 3(2x-5)[3(2x-5) - x]\)

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

\(= 3(2x-5)(5x - 15)\)

\(= 15(2x-5)(x-3)\)

d. \(2xy^3-15x^4=x(2y^3-15x^3)\)

e. \(3x^4-48=3(x^4-16)=3[(x^2)^2-4^2]\)

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

f. \(x^2 - z^2 + 4xy + 4y^2\)

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

\(= (x + 2y)^2 - z^2\)

\(= (x + 2y - z)(x + 2y + z)\)

g. \(x^2 - z^2 + 2xy - 6zt + y^2 - 9t^2\)

\(= (x^2 + 2xy + y^2) - (z^2 + 6zt + 9t^2)\)

\(= (x+y)^2 - (z + 3t)^2\)

\(= [(x+y) - (z+3t)][(x+y) + (z+3t)]\)

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

h. \(x^2-12x+20=x^2-2x-10x+20\)

\(=x(x-2)-10(x-2)=(x-2)(x-10)\)

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

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

3. ta có a vuông góc với AB, b vuông góc với AB

⇒ a // b

ta có góc C1 = góc ACD (đối đỉnh)

mà góc ACD = góc D1 (đồng vị)

nên góc C1 = góc D1 = 110 độ

\(\left( \frac{x}{x^2-36} - \frac{6}{x^2+6x} \right) : \frac{2x-6}{x^2+6x} + \frac{x}{6-x}\) (đkxđ: \(x \neq 0;\ x \neq \pm 6;\ x \neq 3\) )

\(= \left[ \frac{x}{(x-6)(x+6)} - \frac{6}{x(x+6)} \right] \cdot \frac{x(x+6)}{2(x-3)} - \frac{x}{x-6}\)

\(= \frac{x^2 - 6(x-6)}{x(x-6)(x+6)} \cdot \frac{x(x+6)}{2(x-3)} - \frac{x}{x-6}\)

\(= \frac{x^2 - 6x + 36}{x(x-6)(x+6)} \cdot \frac{x(x+6)}{2(x-3)} - \frac{x}{x-6}\)

\(= \frac{x^2 - 6x + 36}{2(x-6)(x-3)} - \frac{x}{x-6}\)

\(= \frac{x^2 - 6x + 36 - 2x(x-3)}{2(x-6)(x-3)}\)

\(= \frac{x^2 - 6x + 36 - 2x^2 + 6x}{2(x-6)(x-3)}\)

\(=\frac{-x^2 + 36}{2(x-6)(x-3)}=\frac{-(x^2 - 36)}{2(x-6)(x-3)}\)

\(=\frac{-(x-6)(x+6)}{2(x-6)(x-3)}=\frac{-(x+6)}{2(x-3)}\)

1. đkxđ: \(x \neq 0;\ x \neq -2;\ x \neq -1\)

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

\(=\frac{x^2+x-2}{x(x+2)}\cdot\frac{x}{x+1}=\frac{(x-1)(x+2)}{x(x+2)}\cdot\frac{x}{x+1}\)

\(= \frac{x-1}{x} \cdot \frac{x}{x+1} = \frac{x-1}{x+1}\)

2. đkxđ: \(x \neq \pm 2;\ x \neq -1\)

\(\left( \frac{x}{x^2-4} + \frac{1}{x+2} - \frac{2}{x-2} \right) : \left( 1 - \frac{x}{x+2} \right)\)

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

\(= \frac{x + x - 2 - 2x - 4}{(x-2)(x+2)} : \frac{2}{x+2}\)

\(=\frac{-6}{(x-2)(x+2)}\cdot\frac{x+2}{2}\)

\(= \frac{-3}{x-2}\)

3. đkxđ: \(x \neq 0;\ x \neq \pm 2;\ x \neq -1\)

\(\left( \frac{4x}{x^2+2x} + \frac{2}{x-2} - \frac{6-5x}{4-x^2} \right) : \frac{x+1}{x-2}\)

\(= \left[ \frac{4}{x+2} + \frac{2}{x-2} + \frac{6-5x}{(x-2)(x+2)} \right] : \frac{x+1}{x-2}\)

\(= \frac{4(x-2) + 2(x+2) + 6 - 5x}{(x-2)(x+2)} \cdot \frac{x-2}{x+1}\)

\(= \frac{4x - 8 + 2x + 4 + 6 - 5x}{(x-2)(x+2)} \cdot \frac{x-2}{x+1}\)

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

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

4. đkxđ: \(x \neq \pm 3;\ x \neq 1\)

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

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

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

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

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

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

5. đkxđ: \(x \neq \pm 3\)

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

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

\(= \frac{x(x-3) + 2x(x+3) - (3x^2+9)}{(x-3)(x+3)} \cdot \frac{x-3}{3}\)

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

\(= \frac{3x - 9}{(x-3)(x+3)} \cdot \frac{x-3}{3}\)

\(= \frac{3(x-3)}{(x-3)(x+3)} \cdot \frac{x-3}{3} = \frac{x-3}{x+3}\)

6. đkxđ: \(x \neq \pm 2;\ x \neq -3\)

\(\left( \frac{1}{x+2} + \frac{5}{x-2} + \frac{4}{x^2-4} \right) : \frac{6}{x+3}\)

\(= \left[ \frac{1}{x+2} + \frac{5}{x-2} + \frac{4}{(x-2)(x+2)} \right] : \frac{6}{x+3}\)

\(= \frac{(x-2) + 5(x+2) + 4}{(x-2)(x+2)} \cdot \frac{x+3}{6}\)

\(= \frac{x - 2 + 5x + 10 + 4}{(x-2)(x+2)} \cdot \frac{x+3}{6}\)

\(= \frac{6x + 12}{(x-2)(x+2)} \cdot \frac{x+3}{6}\)

\(= \frac{6(x+2)}{(x-2)(x+2)} \cdot \frac{x+3}{6} = \frac{x+3}{x-2}\)