[6(x-2)\(^3\)+7(x-2)\(^4\)-9(x-2)\(^5\)]:(2-x)\(^2\)
= [6(x-2)\(^3\) + 7(x-2)\(^4\) - 9(x-2)\(^5\)] : (x-2)\(^2\)
= 6(x-2) + 7(x-2)\(^2\) - 9(x-2)\(^3\)
= 6x - 12 + 7(x\(^2\)-4x+4) - 9(x\(^3\)-6x\(^2\)+12x-8)
= 6x - 12 + 7x\(^2\) - 28x + 28 - 9x3 + 54 - 108x + 72
= -9x3 + 7x2 + (6x-28x-108x) + (-12+28+54+72)
= -9x3 + 7x2 - 130x + 142
1. Tính:
a) ( 3x+1) (3x-1) ; ( x+5y) (x-5y)
b) ( x-3) (x^2+3x+9) ; (x-5) (x^2+5x+25)
2. Rút gọn biểu thức:
a) (x+1) ^2 - (x-1)^2-3 (x+1) (x-1)
b) 5(x+2) (x-2) - (2x-3) ^2-x^2+17
c) (x-1) ^3-(x-1)(x^2+x+1)
d) (x-3) ^3-(x-3)(x^2+3x+9) +6(x+1) ^2
3. Tìm x:
a) (x+4) ^2-(x+1)(x-1) =16
b) (2x-1) ^2+(x+3) ^2-5(x+7) (x-7) = 0
c) (x-2) ^3-(x-4)(x^2+4x+16) +6(x+1) ^2=49
d) (x+2)(x^2-2x+4) -x(x^2+2) =15
1:
1). 2x-3=11-5x
2). 0,5(2x-9)=1,5x(x-5)
3). 28(x-1)-9(x-2)=14x
4). 8(3x-2)-14x=2(4-7x)+18x
5). 2(x-5)-6(1-2x)=3x+2
6). 2x-3=3(x-1)+x+2
1) Thực hiện phép tính
a) (2x+3)^2+(2x-3)^2-(2x+3)(4x-6)+xy
b) (4x^2+4x+1): (2x+1)
2)Phân tích đa thức sau thành nhân tử
x^3-x+3x^2y+3xy^2-y
3) Tìm x
a)4x^2-12x =-9
b) (5-2x)(2x+7) =4x^2-25
c) x^3+27+(x+3)(x-9) =0
d) 4(2x+7)^2-9(x+3)^2=0
4)CMR với mọi số nguyên n thì:
a)n^2(n+1)+2n(n+1) chia hết cho 6
b)(2n-1)^3-(2n-1) chia hết cho 8
c)(n+7)^2-(n-5)^2 chia hết cho 24
Bài 2: Giải các phương trình sau:
1) 4x+20 = 0
2) 3x + 15 = 30
3) 8x-7 = 2x+11
4) 2x+4 ( 36-x ) = 100
5) 2x- ( 3-5x ) = 4(x+3)
6) 3x(x+2) = 3(x-2)2
7) \(\frac{5x-2}{3}\) =3
8) (6x+3) (5x-20) = 0
9) x5 -3x2 +3x-1 = 0
10) \(\frac{2x_{ }-5}{x+5}\) = 3
11) \(\frac{1}{x-2}\)+4 = \(\frac{x-3}{2-x}\)
12) \(\frac{x+2}{x-2}\) -1 = \(\frac{2x}{x\left(x-2\right)}\)
3) Thực hiện phép tính
a) 9 - 4 x/5x + 1 +4x /5x
b) 3/x - 2/x-1
c) 3x+6/4x-12×3x -9/x+2
d)
2x-16y/x+1×12y^2/(x+1)^2
4)Tìm x
a) 3(x-5)-x+5=0
b)x(x-3)+x-6=0
Bài 1:tìm x
a,(x+1)^3+(2-x)(4+2x+x^2)+3x(x+2)=17
b,(x+2)(x^2-2x+4)-x(x^2-2)=15
c,(x-3)^3-(x-3)(x^2+3x+9)+9(x+1)^2=15
d,x(x-5)(x+5)-(x+2)(x^2-2x+4)=3
Tìm x:
a) \(3x\left(3x-8\right)-9x^2+8=0\)
b)\(6x-15-x\left(5-2x\right)=0\)
c) \(x^3-16x=0\)
d) \(2x^2+3x-5=0\)
e) \(3x^2-x\left(3x-6\right)=36\)
f) \(\left(x+2\right)^2-\left(x-5\right)\left(x+1\right)=17\)
g) \(\left(x-4\right)^2-x\left(x+6\right)=9\)
h) \(4x\left(x-1000\right)-x+1000=0\)
i) \(x^2-36=0\)
j) \(x^2y-2+x+x^2-2y+xy=0\)
k) \(x\left(x+1\right)-\left(x-1\right).\left(2x-3\right)=0\)
l) \(3x^3-27x=0\)
1) Phân tích đa thức thành nhân tử
a) x^3 - x^2 - 4x^2 + 8x + 4
b) 4x^2 - 25 - ( 2x - 5 ) ( 2x + 7)
c) x^3 + 27 + ( x+3) ( x-9)
d) 4x^2y^2 - ( x^2 + y^2 - z^2 )^2
phân tích các đa thức sau thành nhân tử:
x^3-x^2-4x^2+8x-4
4x^2-25-(2x-5)(2x+7)
x^3+27+(x+3)(x-9)
4x^2y^2-(x^2+y^2-z^2)^2
