Câu 1: Rút gọn các biểu thức sau:

1. \(\left(x+y-z\right)^2+\left(y-z\right)^2+2z\left(z-y\right)\)

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

3.\(\left(3+1\right)\left(3^2+1\right)\left(3^4+1\right)\left(3^8+1\right)\left(3^{16}+1\right)\left(3^{32}+1\right)\)

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

5. \(\left(3+1\right)\left(3^2+1\right)\left(3^4+1\right)\left(3^8+1\right)\left(3^{16}+1\right)\left(3^{32}+1\right)\)

Câu 2: Tìm x

1. \(4\left(x+1\right)^2+\left(2x-1\right)^2-8\left(x-1\right)\left(x+1\right)=1\)

2. \(\left(3x+1\right)^2+\left(5x-2\right)^2=34\left(x+2\right)\left(x-2\right)\)

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

4. \(4x^2-9-x\left(2x-3\right)=0\)

5. \(4x^2-12x+9=0\)

Câu 3: Tìm GTNN

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

Câu 4: Cho \(a^2+b^2+c^2=ab+bc+ac\) . Chứng minh rằng a=b=c

Tìm x biết : (đề không sai)

1.\(-4x\left(x-7\right)+4x\left(x^2-5\right)\) \(=28x^2-13\)

2.\(\left(4x^2-5x\right)\left(3x+2\right)-7x\left(x-7\right)\)= \(\left(-4+x\right)\left(-2x+3\right)+12x^3+2x^2\)

3.\(\left(-4x^2-3\right)\left(2x+5\right)-\left(8x-3\right)\) \(\left(-x^2+2\right)=-5x^2\left(x-6\right)-3x^2-4\)

4.\(\left(x-7\right)\left(x+5\right)-\left(x-3\right)\left(x-2\right)\) \(=15x^2\left(x+1\right)-\left(3x^2-1\right)\) \(\left(5x^2-2\right)-21x^2\)

5.\(\left(x-3\right)\left(-x+10\right)+\left(x-8\right)\left(x+3\right)\) \(=\left(5x^2-1\right)\left(x+3\right)-5x^3-15x^2\)

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

Tìm số nguyên x

1/ \(17x+3\left(-16x-37\right)=2x+43-4x\)

2/ \(-2x-3\left(x-17\right)=34-2\left(-x+25\right)\)

3/ \(\left\{-3x+2\left[45-x-3\left(3x+7\right)-2x\right]+4x\right\}=55-103-57:\left[-2\left(2x-1\right)^2-\left(-9\right)^0\right]=-106\)

4/ \(-2x+3\left\{12-2\left[3x-\left(20+2x\right)-4x\right]+1\right\}=45\)

5/ \(3x-32>-5+1\)

6/ \(15+4x< 2x-145\)

7/ \(-3\left(2x+5\right)-16< -4\left(3-2x\right)\)

8/ \(-2x+15< 3x-7< 19-x\)

Rút gọn các biểu thức: 

\(A=\left(x+3\right)\left(x^2-3x+9\right)-\left(54+x^3\right)\)

\(B=\left(2x+y\right)\left(4x^2-2xy+y^2\right)-\left(2x-y\right)\left(4x^2+2xy+y^2\right)\)

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

\(D=\left(x-2\right)\left(x^2+2x+4\right)-\left(x+1\right)^3+3\left(x-1\right)\left(x+1\right)\)

BÀI 6 tìm x

1,\(2x\left(x-5\right)-\left(3x+2x^2\right)=0\)                          2,\(x\left(5-2x\right)+2x\left(x-1\right)=13\)

3,\(2x^3\left(2x-3\right)-x^2\left(4x^2-6x+2\right)=0\)            4,\(5x\left(x-1\right)-\left(x+2\right)\left(5x-7\right)=6\)

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