a) \(^{ }\left(7x+4\right)^2-\left(7x-4\right)\left(7x+4\right)\)
b) \(^{ }8\left(x-2\right)-3\left(x^2-4x-5\right)-5x^2\)
c) \(^{^{ }}\left(x+1\right)^3-\left(x-1\right)\left(x^2+x+1\right)-3x\left(x+1\right)\)
Tính:
a) \(\left(x^2-2\right).\left(1-x\right)+\left(x+3\right).\left(x^2-3x+9\right)\)
b) \(\left(2x^4+x^3-3x^2+4x-3\right):\left(x^2-x+1\right)\)
Giải các phương trình sau:
f. 5 – (x – 6) = 4(3 – 2x)
g. 7 – (2x + 4) = – (x + 4)
h. \(2x\left(x+2\right)^2-8x^2=2\left(x-2\right)\left(x^2+2x+4\right)\)
i. \(\left(x-2^3\right)+\left(3x-1\right)\left(3x+1\right)=\left(x+1\right)^3\)
k. (x + 1)(2x – 3) = (2x – 1)(x + 5)
rút gọn biểu thức sau bằng cách nhanh nhất
A = \(\left(a^2+b^2-c^2\right)^2-\left(a^2-b^2+c^2\right)^2-4a^2b^2\)
B = \(\left(3x^3+3x+1\right)\cdot\left(3x^3-3x+1\right)-\left(3x^3+1\right)^2\)
C = \(\left(2-6x\right)^2+\left(2-5x\right)^2+2\cdot\left(6x-2\right)\cdot\left(2-5x\right)\)
D = \(5\cdot\left(3x-1\right)^2+4\cdot\left(5x+1\right)^2-12\cdot\left(5x-2\right)\left(5x+2\right)\)
E = \(\left(3x-1\right)^2+\left(2x+4\right)\cdot\left(1-3x\right)+\left(x+2\right)^2\)
G = \(\left(x-1\right)^3+4\cdot\left(x+1\right)\cdot\left(1-x\right)+3\cdot\left(x-1\right)\cdot\left(x^2+x+1\right)\)
d) \(^{ }4x\left(2x+3\right)-8x\left(x+4\right)\)
e) \(^{ }2x\left(5x+2\right)+\left(2x-3\right)\left(3x-1\right)\)
f) \(^{ }x\left(x+2\right)^2-\left(x+1\right)^3+3\left(x-1\right)\left(x+1\right)\)
Rút gọn các biểu thức sau:
a/\(\left(3x-1\right)^2-2\left(2-5x\right)^2-2\left(x^2+x-1\right)\left(x-1\right)\)
b/\(\left(3a-1\right)^2+2\left(9a^2-1\right)+\left(3a-1^{ }\right)^2\)
c/\(\left(3x-4^{ }\right)^2+\left(4-x\right)^2-2\left(3x-4\right)\left(x-4\right)\)
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 \(x\):
\(8\)) \(1-\left(x-6\right)=4\left(2-2x\right)\)
\(9\))\(\left(3x-2\right)\left(x+5\right)=0\)
\(10\))\(\left(x+3\right)\left(x^2+2\right)=0\)
\(11\))\(\left(5x-1\right)\left(x^2-9\right)=0\)
\(12\))\(x\left(x-3\right)+3\left(x-3\right)=0\)
\(13\))\(x\left(x-5\right)-4x+20=0\)
\(14\))\(x^2+4x-5=0\)
Giải các bất phương trình sau :
\(a.4\left(x-3\right)^2-\left(2x-1\right)^2\ge12\)
\(b.\left(x-4\right)\left(x+4\right)\ge\left(x+3\right)^2+5\)
c. \(\left(3x-1\right)^2-9\left(x+2\right)\left(x-2\right)< 5x\)
Tính
\(\left(x-y\right)\left(x+y\right)\left(x^2+y^2\right)\left(x^4+y^4\right)\)
\(2x^2\left(x-2\right)+3x\left(x^2-x-2\right)-5\left(3-x^2\right)\)
\(\left(x-1\right)\left(x-3\right)-\left(4-x\right)\left(2x+1\right)-3x^2+2x-5\)
