Rút gọn biểu thức
E=2.|x-3|-4x-1|
H=|2x+3|-|x-1|+3x
Rút gọn biểu thức
e) (x+1)2 + (x – 1)2 – 2(1 + x)(1 x)
f) 2x(2x – 1)2 – 3x(x+3)(x – 3) – 4x(x+1)2
g) 3(x + 2)2 – (3x + 1)(x + 5) + (x + 5)2
f: Ta có: \(2x\left(2x-1\right)^2-3x\left(x+3\right)\left(x-3\right)-4x\left(x+1\right)^2\)
\(=2x\left(4x^2-4x+1\right)-3x\left(x^2-9\right)-4x\left(x^2+2x+1\right)\)
\(=8x^3-8x^2+2x-3x^3+27x-4x^3-8x^2-4x\)
\(=x^3-16x^2+25x\)
g: Ta có: \(3\left(x+2\right)^2-\left(3x+1\right)\left(x+5\right)+\left(x+5\right)^2\)
\(=3\left(x^2+4x+4\right)-\left(3x^2+16x+5\right)+x^2+10x+25\)
\(=3x^2+12x+12-3x^2-16x-5+x^2+10x+25\)
\(=x^2+6x+32\)
e) (x+1)2+(x-1)2-2(1+x)(1-x)
= (x+1)2 + 2(1+x)(x-1) + (x-1)2
= (x+1+x-1)2
= 4x2
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 sau:
a. (x+5)2-4x(2x+3)2-(2x-1)(x+3)(x-3)
b. -2x(3x+2)(3x-2)+5(x+2)2-(x-1)(2x-1)(2x+1)
a: Ta có: \(\left(x+5\right)^2-4x\left(2x+3\right)^2-\left(2x-1\right)\left(x+3\right)\left(x-3\right)\)
\(=x^2+10x+25-4x\left(4x^2+12x+9\right)-\left(2x-1\right)\left(x^2-9\right)\)
\(=x^2+10x+25-16x^3-48x^2-36x-2x^3+18x+x^2-9\)
\(=-18x^3-46x^2-8x+16\)
Bài I. Rút gọn các biểu thức sau:
a) 3x(2x+1)+ (2x - 3)(x+1),
b) x(3x - 2)2 + 3(x-2)(x+2)
c) (2x+1)(4x² - 2x+1)-2x(2x+3)(2x - 3)-(x-3)²
a: Ta có: \(3x\left(2x+1\right)+\left(2x-3\right)\left(x+1\right)\)
\(=6x^2+3x+2x^2+2x-3x-3\)
\(=8x^2+2x-3\)
rút gọn biểu thức:(8x^3-4x^2):4x-(4x^2-5x):(2x)+(2x)^2
(3x^3-x^2y):x^2-(xy^2+x^2y):(xy)+2x(x-1)
a: Ta có: \(\left(8x^3-4x^2\right):4x-\left(4x^2-5x\right):2x+\left(2x\right)^2\)
\(=2x^2-x-2x+\dfrac{5}{2}+4x^2\)
\(=6x^2-3x+\dfrac{5}{2}\)
b: Ta có: \(\left(3x^3-x^2y\right):x^2-\left(xy^2+x^2y\right):xy+2x\left(x-1\right)\)
\(=3x-y-y-x+2x^2-2x\)
\(=2x^2-2y\)
rút gọn biểu thức (3+x/3-x+2x/3+x -4x^2-3x-9/x^2-9):(2/3-x -x-1/3x-x^2)
(\(3+\dfrac{x}{3-x}+\dfrac{2x}{3+x}-\dfrac{4x^2-3x-9}{x^2-9}\) ):\(\left(\dfrac{2}{3-x}-\dfrac{x-1}{3x-x^2}\right)\)\(=\left(\dfrac{3x^2-27}{\left(x-3\right)\left(x+3\right)}+\dfrac{-x\left(x+3\right)}{\left(x-3\right)\left(x+3\right)}+\dfrac{2x\left(x-3\right)}{\left(x-3\right)\left(x+3\right)}-\dfrac{4x^2-3x-9}{\left(x-3\right)\left(x+3\right)}\right)\)\(:\left(\dfrac{2x}{x\left(3-x\right)}-\dfrac{x-1}{x\left(3-x\right)}\right)\)
\(=\dfrac{3x^2-27-x^2-3x+2x^2-6x-4x^2+3x+9}{\left(x-3\right)\left(x+3\right)}:\dfrac{x+1}{x\left(3-x\right)}\)
\(=\dfrac{-6x-18}{\left(x-3\right)\left(x+3\right)}:\dfrac{x+1}{x\left(3-x\right)}\) \(=\dfrac{-6\left(x+3\right)}{\left(x-3\right)\left(x+3\right)}:\dfrac{x+1}{x\left(3-x\right)}\)
\(=\dfrac{6}{3-x}.\dfrac{x\left(x-3\right)}{x+1}\) \(=\dfrac{6x}{x+1}\)
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: \(3\left(x+2\right)^2-\left(3x+1\right)\left(x+5\right)+\left(x+5\right)^2\)
\(=3x^2+12x+12-3x^2-16x-5+x^2+10x+25\)
\(=x^2+6x+32\)
Bài 1:Rút gọn biểu thức
1,3x(4x-3)-(2x-1)(sáu x +5)
2,2(3x-1)(2x+5)-(4x-1)(3x-2)
3,(3x-5)(2+11)-(2x+3)(3x+7)
4,(x-5)(2x+3)-2x(x-3)+x+7
Rút gọn biểu thức
a) (x-3)(3x+2)-3x(x-5)+3
b) 2x(x-3)-(x-5)(2x-1)
c) (3x+2)(3x-2)+(4x-1)(x+2)-3
a) \(\left(x-3\right)\left(3x+2\right)-3x\left(x-5\right)+3\)
\(=x.\left(3x+2\right)-3.\left(3x+2\right)-3x\left(x-5\right)+3\)
\(=x.3x+x.2-3.3x-3.2-3x.x+3x.5+3\)
\(=3x^2+2x-9x-6-3x^2+15x+3\)
\(=8x-3\)
b )
\(2x\left(x-3\right)-\left(x-5\right)\left(2x-1\right)\)
\(2x.x-2x.3-x.\left(2x-1\right)-5.\left(2x-1\right)\)
\(2x.x-2x.3-x.2x+x.1-5.2x+5.x\)
\(2x^3-6x-2x^2+x-10x+5x\)
\(2x^3-15x-2x^2\)
muốn nhân đa thức với đa thức khỏi cần phải nhân từng đa thức với đơn thức .... Thì ta nhân luôn .... Lấy cả dấu mà nhân:
VD: \(\left(x-5\right)\left(2x-1\right)=x.2x+\left(-5\right).2x+x.\left(-1\right)+\left(-5\right)\left(-1\right)\)
Nhưng khi biết rồi thì nhẩm rồi viết ra kết quả cuối cho nhanh .... còn các câu hình như đồng dạng đó
Rút gọn biểu thức
2x(3x^3-x)-4x^2(x-x^2+1)+(x-3x^2)x
2x(3x3-x)-4x2(x-x2+1)+(x-3x2)x
=6x4-2x2+4x4-4x3-4x2+x2-3x3
=(6x4+4x4)+(-4x3-3x3)+(-4x2-x2)
=10x4-7x3-5x2
\(2x\left(3x^3-x\right)-4x^2\left(x-x^2+1\right)+\left(x-3x^2\right)x\\ =6x^4-2x^2+4x^4-4x^3-4x^2+x^2-3x^3\\ =\left(6x^4+4x^4\right)+\left(-4x^3\right)-3x^3+\left(-4x^2-x^2\right)\)
\(=10x^4-7x^3-5x^2\)