Rút gọn tổng: \(P=1+2x+3x^2+4x^3+...+100x^{99}\)
1. Tính giá trị các biểu thức sau :
A = 4x2 - 5. |x| + 2. |3-x| tại x= 5, x = -3
B = xy + x2y2 + x3y3 + ... + x100y100 tại x =1 , y = -1
C = 100x100 + 99x99 + 98x98 + ... + 2x2 + x tại x = 1
D = x99 - 100x98 + 100x97 - 100x96 + .... + 100x - 1 tại x =99
2. Rút gọn các đa thức sau
a) x (4x2 - 2x + 1) - 5y (X2 + 2x) + 10xy
b) ( x2 - xy + y2). 2x + 3y (x2 - xy - y2)
c) (x-2) (x+2)
d) x2 ( x+ y) - y ( x2 - y2)
1,+) Thay x = 5 vào biểu thức A, ta có:
A = 4.52 - 5.|5| + 2.|3 - 5|
A = 4.25 - 5.5 + 2.2
A = 100 - 25 + 4
A = 75 + 4 = 79
Thay x = 3 vào biểu thức A, ta có:
A = 4.32 - 5.|3| + 2.|3 - 3|
A = 4.9 - 5.3 + 2.0
A = 36 - 15 = 21
+) Ta có: B = xy + x2y2 + x3y3 + ... + x100y100
B = xy + (xy)2 + (xy)3 + ... + (xy)100
Thay x = 1; y= -1 vào biểu thức B, ta có:
B = 1.(-1) + [1.(-1)]2 + [1.(-1)]3 + ... + [1.(-1)]100
B = -1 + 1 - 1 + ... + 1
B = 0
+) Thay x = 1 vào C, ta có:
C = 100.1100 + 99.199 + 98.198 + ... + 2.12 + 1
C = 100 + 99 + 98 + ... + 2 + 1
C = (100 + 1).[(100 - 1) : 1 + 1] : 2
C = 101.100 : 2
C = 5050
+) Thay x = 99 vào biểu thức D, ta có:
D = 9999 - 100.9998 + 100.9997 - 100.9996 + ... + 100.99 - 1
D = 9999 - (99 + 1).9998 + (99 + 1).9997 - (99 + 1).9996 + ... + (99 + 1).99 - 1
D = 9999 - 9999 - 9998 + 9998 + 9997 - 9997 - 9996 + ... + 992 + 99 - 1
D = 99 - 1 = 98
Rút gọn
a, (3x+2).(3x+2) - (3x+1)\(^2\)
b, (1-4x\(^2\)).(1+4x\(^2\))-(2x+3)\(^2\)
a) \(\left(3x+2\right)\left(3x+2\right)-\left(3x+1\right)^2=\left(3x+2\right)^2-\left(3x+1\right)^2=\left(3x+2-3x-1\right)\left(3x+2+3x+1\right)=1.\left(6x+3\right)=6x+3\)
b) \(\left(1-4x^2\right)\left(1+4x^2\right)-\left(2x+3\right)^2=1-16x^4-4x^2-12x-9=-16x^4-4x^2-12x-8\)
a: \(\left(3x+2\right)\left(3x+2\right)-\left(3x+1\right)^2\)
\(=9x^4+12x+4-9x^2-6x-1\)
=6x+3
b: \(\left(1-4x^2\right)\left(1+4x^2\right)-\left(2x+3\right)^2\)
\(=1-16x^4-4x^2-12x-9\)
\(=-16x^4-4x^2-12x-8\)
Rút gọn
a, (x-2).(3x-1).(3x+1)-2x.(4x-3)^2
b, ( 5x-7)^2 - ( 4x -3).(2x+3)^2- (x-3).(3x^2-5)
c, (2-5x)^2-4x.(3x+1)^2-(x-3).(x+3)
1/2x1+1/3x(1+2)+1/4x(1+2+3)+...+1/100x(1+2+3+...+99+100)
Giup minh voi
Rút gọn
a, (x-2).(3x-1).(3x+1)-2x.(4x-3)^2
b, ( 5x-7)^2 - ( 4x -3).(2x+3)^2- (x-3).(3x^2-5)
c, (2-5x)^2-4x.(3x+1)^2-(x-3).(x+3)
rút gọn 2x(2x-1)^2 - 3x(x+3)(x-3)-4x(x+1)^2
1) rút gọn
a) (x^2-2x+2)(x^2-2)(x^2+2x+2)(x^2+2)
b) (x+1)^2-(x-1)^2+3x^3-3x(x+1)(x-1)
c) (2x+1)^2+2(4x^2-1)+(2x+1)^2
d) (3x+1)^2-2(3x+1)(3x+5)+(3x+5)^2
e) (a-b+c)^2-2(a-b+c)(c-b)+(b-c)^2
f)(2x-5)(4x^2+10x+25)(2x+5)(4x^2-10x+25)
g)(a+b)^3+(a-b)^3-2a^3
h) 100^2-99^2+98^2-97^2+....+2^2 -1
tính (rút gọn )
2x(3x-1)-(2x+1)(x-3)
3(x^2-2x)-(4x+2)(x-1)
Ta có: \(2x\left(3x-1\right)-\left(2x+1\right)\left(x-3\right)\)
\(=6x^2-2x-\left(2x^2-6x+x-3\right)\)
\(=6x^2-2x-2x^2+5x+3\)
\(=4x^2+3x+3\)
Ta có: \(3\left(x^2-2x\right)-\left(4x+2\right)\left(x-1\right)\)
\(=3x^2-6x-\left(4x^2-4x+2x-2\right)\)
\(=3x^2-6x-4x^2+2x+2\)
\(=-x^2-4x+2\)
\(2x\left(3x-1\right)-\left(2x+1\right)\left(x-3\right)=6x^2-2x-2x^2+5x+3=4x^2+3x+3\)
\(3\left(x^2-2x\right)-\left(4x+2\right)\left(x-1\right)=3x^2-6x-4x^2+2x-2=-x^2-4x-2\)
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rút gọn 2x(2x-1)^2 - 3x(x+3)(x-3)-4x(x+1)^2
2x(2x-1)^2-3x(x+3)(x-3)+4x(x-1)
2x(4x^2 - 4x + 1) - 3x(x^2 - 9) + 4x^2 - 4x
= 8x^3 - 8x^2 + 2x - 3x^3 + 27x + 4x^2 - 4x
= (8x^3 - 3x^3) + (-8x^2+ 4x^2) + (2x +27x - 4x)
= 5x^3 - 4x^2 + 25x
= x(5x^2 - 4x + 25)
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