1) Rút gọn biểu thức:
a) A = |2x+3| + |x-7| + |6-x| + |8x-3|
b) B = |x+1| + |1-x| + |x+2| + |3-x|
Rút gọn biểu thức:
a) (x+2)(x-2)-(x-3)(x+1)
b) (x2-5)(x+3)+(x+4)(x-x2)
c)(x-5)(2x+3)-2x(x-3)+x+7
d)(2x+1)2+(3x-1)2+2(2x+1)(3x-1)
\(a,=x^2-4-x^2+2x+3=2x-1\\ b,=x^3+3x^2-5x-15+x^2-x^3+4x-4x^2=-x-15\\ c,=2x^2+3x-10x-15-2x^2+6x+x+7=-8\\ d,=\left(2x+1+3x-1\right)^2=25x^2\)
Rút gọn biểu thức:
a) (x+1)2 + (x – 1)2 – 2(1 + x)(1 - x)
b) 2x(2x – 1)2 – 3x(x+3)(x – 3) – 4x(x+1)2
c) 3(x + 2)2 – (3x + 1)(x + 5) + (x + 5)2
a: Ta có: \(\left(x+1\right)^2+\left(x-1\right)^2-2\left(1+x\right)\left(1-x\right)\)
\(=\left(x+1\right)^2+2\left(x+1\right)\left(x-1\right)+\left(x-1\right)^2\)
\(=\left(x+1+x-1\right)^2\)
\(=4x^2\)
c: Ta có: \(3\left(x+2\right)^2-\left(3x+1\right)\left(x+5\right)+\left(x+5\right)^2\)
\(=3x^2+12x+12-3x^2-16x-5+x^2+10x+25\)
\(=x^2+6x+32\)
rút gọn các biểu thức:
a) (x-2)2-(2x-1)2+(3x-1)(x-5)
b) (x-3)3-(x+3)(x2-3x+9)+(3x-1)(3x+1)
a: Ta có: \(\left(x-2\right)^2-\left(2x-1\right)^2+\left(3x-1\right)\left(x-5\right)\)
\(=x^2-4x+4-4x^2+4x-1+3x^2-15x-x+5\)
\(=-16x+8\)
b: Ta có: \(\left(x-3\right)^3-\left(x+3\right)\left(x^2-3x+9\right)+\left(3x-1\right)\left(3x+1\right)\)
\(=x^3-9x^2+27x-27-x^3-27+9x^2-1\)
=27x-55
Rút gọn biểu thức:
a) A=(x-y)2+(x+y)2
b) B=(2x-1)2-2(2x-3)2+4
a, \(A=\left(x-y\right)^2+\left(x+y\right)^2\)
\(=x^2-2xy+y^2+x^2+2xy+y^2\)
\(=2x^2+2y^2\)
a) \(A=\left(x-y\right)^2+\left(x+y\right)^2\\ =x^2-2xy+y^2+x^2+2xy+y^2=2x^2+2y^2\)
b) \(B=\left(2x-1\right)^2-2\left(2x-3\right)^2+4\\ =4x^2-4x+1-2\left(4x^2-12x+9\right)+4\\ =4x^2-4x+1-8x^2+24x-18+4\)
\(=-4x^2+20x-13\)
cho biểu thức:A=[(1/x-1)+(x/x^3-1).(x^2+x+1/x+1)]:2x+1/x^2+2x+1
a,rút gọn biểu thức A
b,tính giá trị của biểu thức khi x=1/2
\(ĐKXĐ:\hept{\begin{cases}x\ne\pm1\\x\ne-\frac{1}{2}\end{cases}}\)
a) \(A=\left(\frac{1}{x-1}+\frac{x}{x^3-1}\cdot\frac{x^2+x+1}{x+1}\right):\frac{2x+1}{x^2+2x+1}\)
\(\Leftrightarrow A=\left(\frac{1}{x-1}+\frac{x}{\left(x-1\right)\left(x+1\right)}\right):\frac{2x+1}{\left(x+1\right)^2}\)
\(\Leftrightarrow A=\frac{x+1+x}{\left(x-1\right)\left(x+1\right)}\cdot\frac{\left(x+1\right)^2}{2x+1}\)
\(\Leftrightarrow A=\frac{\left(2x+1\right)\left(x+1\right)}{\left(x-1\right)\left(2x+1\right)}\)
\(\Leftrightarrow A=\frac{x+1}{x-1}\)
b) Thay \(x=\frac{1}{2}\)vào A, ta được :
\(A=\frac{\frac{1}{2}+1}{\frac{1}{2}-1}=\frac{\frac{3}{2}}{-\frac{1}{2}}=-3\)
1. Rút gọn biểu thức:
a) (x+2) (x2- 2x + 4) - (x3- 2)
b) (x+5)2 - 4x ( 2x+3)2 - ( 2x-1) (x+3) (x-3)
2 Tính nhanh:
1272 + 146.127 +7322
\(a.x^3+8-x^3+2=10\)
\(b.x^2+10x+25-4x\left(4x^2+12x+9\right)-\left(2x-1\right)\left(x^2-9\right)=x^2+10x+25-16x^3-28x^2-36x-2x^3+18x+x^2-9=-18x^3-26x^2-8x+16=\)
rút gọn biểu thức:
a) \(\dfrac{2x^{2^{ }}-2x}{x-1}\)
b)\(\dfrac{x^{2^{ }}+2x+1}{3x^2+3x}\)
c)\(\dfrac{x}{3x-3}+\dfrac{1}{x^2-1}\)
a) Ta có: \(\dfrac{2x^2-2x}{x-1}\)
\(=\dfrac{2x\left(x-1\right)}{x-1}\)
=2x
b) Ta có: \(\dfrac{x^2+2x+1}{3x^2+3x}\)
\(=\dfrac{\left(x+1\right)^2}{3x\left(x+1\right)}\)
\(=\dfrac{x+1}{3x}\)
c) Ta có: \(\dfrac{x}{3x-3}+\dfrac{1}{x^2-1}\)
\(=\dfrac{x}{3\left(x-1\right)}+\dfrac{1}{\left(x-1\right)\left(x+1\right)}\)
\(=\dfrac{x+1+3}{3\left(x-1\right)\left(x+1\right)}\)
\(=\dfrac{x+4}{3x^2-3}\)
a, \(\dfrac{2x^2-2x}{x-1}=\dfrac{2x\left(x-1\right)}{x-1}=2x\) ( đk : \(x\ne1\) )
b,\(\dfrac{x^2+2x+1}{3x^2+3x}=\dfrac{\left(x+1\right)^2}{3x\left(x+1\right)}=\dfrac{x+1}{3x}\) ( đk : \(x\ne-1\) )
c
=
Câu 1. Khai triển các biểu thức:
a) (a-b+c)2 b) (a+2b-c)2
c) (2a-b-c)2
Câu 2. Rút gọn biểu thức:
a) A=(x-y)2+(x+y)2
b) B=(2x-1)2-2(2x-3)2+4
Câu 3. Tính nhanh:
a) 492 b) 512
c) 99.100
Câu 4. Tìm x, biết:
a) 16x2-(4x-5)2=15 b) (2x+1)(1-2x)+(1-2x)2=18
c) (x-5)2-x(x-4)=9 d) (x-5)2+(x-4)(1-x)=0
Tách ra mỗi câu một lần.
Dài quá không ai làm đâu.
Nhìn nản lắm.
Câu 3:
a: \(49^2=2401\)
b: \(51^2=2601\)
c: \(99\cdot100=9900\)
Bài 2: Rút gọn biểu thức:
a/ A = (3x–1)2 + (x+3)(2x–1)
b/ B = x(x–y) + y(x–y)
e/ C = (x–2)(x2+2x+ 4) – x(x2 –2)
f/ D = (x+y)2– (x–y)2
\(a.\left(3x-1\right)^2+\left(x+3\right)\left(2x-1\right)\)
\(=9x^2-6x+1-2x^2+x-6x+3\)
\(=7x^2-11x+4\)