-2(3x+1)+3(4x+2)=5(6x-3)
4x(5x − 2) 7x Ä 3x 2 − 6x + 2ä b) c) 2x(3x + 2) + (4x + 3)(2x − 1) 3x 3 y 2 : x 2 d) Ä x 3 + 4x 3 − 6x 2 ä : 4x 2 e) Ä 3x 2 − 6x ä f) : (2 − x) Ä 6x 2 + 13x − 5 ä g) : (2x + 5) Ä x 3 − 3x 2 + x − 3 ä h) : (x − 3)
Tìm x:
1) -3.(1-2x) - 4.(1+3x) = -5x + 5
2) 3.(2x - 5) - 6.(1 - 4x) = -3x + 7
3) (1 - 3x) - 2.(3x - 6) = -4x - 5
4) x.(4x - 3) - 2x.(2x - 1) = 5x - 7
5) 3x.(2x - 1) - 6x.(x + 2) = -3x + 4
6) (1 - 2x).3 - 4.(6x - 1) = 7x - 5
7) 6x - 3.(1 - 4x) - 5.(x + 1) = 2x + 7
8) 6.(1 - 3x) - 3.(2x + 5) = -10x + 7
9) 3x.(1 - 2x) + 6x^2 - 7x = 8.(1 - 2x) - 9
10) 2x.(1 + 3x) - 3x.(4 + 2x) = 3x - 4
* Trả lời:
\(\left(1\right)\) \(-3\left(1-2x\right)-4\left(1+3x\right)=-5x+5\)
\(\Leftrightarrow-3+6x-4-12x=-5x+5\)
\(\Leftrightarrow6x-12x+5x=3+4+5\)
\(\Leftrightarrow x=12\)
\(\left(2\right)\) \(3\left(2x-5\right)-6\left(1-4x\right)=-3x+7\)
\(\Leftrightarrow6x-15-6+24x=-3x+7\)
\(\Leftrightarrow6x+24x+3x=15+6+7\)
\(\Leftrightarrow33x=28\)
\(\Leftrightarrow x=\dfrac{28}{33}\)
\(\left(3\right)\) \(\left(1-3x\right)-2\left(3x-6\right)=-4x-5\)
\(\Leftrightarrow1-3x-6x+12=-4x-5\)
\(\Leftrightarrow-3x-6x+4x=-1-12-5\)
\(\Leftrightarrow-5x=-18\)
\(\Leftrightarrow x=\dfrac{18}{5}\)
\(\left(4\right)\) \(x\left(4x-3\right)-2x\left(2x-1\right)=5x-7\)
\(\Leftrightarrow4x^2-3x-4x^2+2x=5x-7\)
\(\Leftrightarrow-x-5x=-7\)
\(\Leftrightarrow-6x=-7\)
\(\Leftrightarrow x=\dfrac{7}{6}\)
\(\left(5\right)\) \(3x\left(2x-1\right)-6x\left(x+2\right)=-3x+4\)
\(\Leftrightarrow6x^2-3x-6x^2-12x=-3x+4\)
\(\Leftrightarrow-15x+3x=4\)
\(\Leftrightarrow-12x=4\)
\(\Leftrightarrow x=-\dfrac{1}{3}\)
1)6x-8=3x+1
2)12-10x=25-30x
3)3(2x+3)-2(4x-5)=10x+21
4)5(5x-3)-3(2x-4)11-5x
5)4(2-3x)-5(1-2x)=4-6x
6)8(4x-3)-3(2-3x)=13-40x
7)10x-5(1-4x)=5x-11
8)-3(3-4x)-5(4-3x)=12x-50
9)-2(20x-3)-3(4x-5)=9-2(2x-3)
10)-5(2-3x)+3(5-2x)=3x+3(3-5x)
1)6x-8=3x+1
6x-3x=1+8
3x=9
x=3
Vậy x=3
2: 12-10x=25-30x
=>20x=13
=>x=13/20
3: \(3\left(2x+3\right)-2\left(4x-5\right)=10x+21\)
=>6x+9-8x+10=10x+21
=>10x+21=-2x+19
=>12x=-2
=>x=-1/6
4: \(\Leftrightarrow25x-15-6x+12=11-5x\)
=>19x-3=11-5x
=>24x=14
=>x=7/12
5: \(\Leftrightarrow8-12x-5+10x=4-6x\)
=>4-6x=-2x+3
=>-4x=-1
=>x=1/4
6: \(\Leftrightarrow32x-24-6+9x=13-40x\)
=>41x-30=13-40x
=>81x=43
=>x=43/81
7: \(\Leftrightarrow10x-5+20x=5x-11\)
=>30x-5=5x-11
=>25x=-6
=>x=-6/25
B1 :Tính
a) (6x^4 - 4x^2 + 3x -2) : (3x - 2)
b) (6x^3 +3x^2 +4x+2) : (3x^2+2)
c) (x^5 +4x^3 +3x^2 - 5x +15 ): ( x^3 -x +3
làm phép chia :
a) (x^4 -2x^3 + 2x -1) : (x^2 - 1)
b) (x^3 -8) : (x^2 + 2x +4)
c) (x^6 - 2x^5 + 2x^4 + 6x^3 - 4x^2)n: 6x^2
d) (-2x^5 + 3x^2 - 4x^3) :2x^2
e) (15x^3 - 10x^2 + x - 2) : (x - 2)
f) (2x^4 - 3x^3 - 3x^2 + 6x - 2) : (x^2 - 2)
b: =x-2
d: \(=-x^3+\dfrac{3}{2}-2x\)
1/ Phân tích đa thức thành nhân tử:
a/x^3 + 4x^2 - 29x +24
b/x^4 +6x^3 +7x^2 - 6x +1
c/(x^2 -x +2)^2 + (x-2)^2
d/6x^5 + 15x^4 + 20x^3 + 15x^2 + 6x +1
e/x^6 + 3x^5 + 4x^4 + 4x^3 + 4x^2 + 3x +1
a) \(x^3+4x^2-29x+24=x^3-x^2+5x^2-5x-24x+24\)
\(=x^2\left(x-1\right)+5x\left(x-1\right)-24\left(x-1\right)\)
\(=\left(x-1\right)\left(x^2+5x-24\right)\)
\(=\left(x-1\right)\left(x^2+8x-3x-24\right)\)
\(=\left(x-1\right)\left[x\left(x+8\right)-3\left(x+8\right)\right]\)
\(=\left(x-1\right)\left(x+8\right)\left(x-3\right)\)
b) \(x^4+6x^3+7x^2-6x+1\)
\(=x^4+\left(6x^3-2x^2\right)+\left(9x^2-6x+1\right)\)
\(=x^4+2x^2\left(3x-1\right)+\left(3x-1\right)^2\)
\(=\left(x^2+3x-1\right)^2\)
c) \(\left(x^2-x+2\right)^2+\left(x-2\right)^2=x^4-2x^3+6x^2-8x+8\)
\(=\left(x^4-2x^3+2x^2\right)+\left(4x^2-8x+8\right)\)
\(=x^2\left(x^2-2x+2\right)+4\left(x^2-2x+2\right)\)
\(=\left(x^2-2x+2\right)\left(x^2+4\right)\)
d) Phức tạp mà dài quá :v
\(6x^5+15x^4+20x^3+15x^2+6x+1\)
\(=6x^5+3x^4+12x^4+6x^3+14x^3+7x^2+8x^2+4x+2x+1\)
\(=3x^4\left(2x+1\right)+6x^3\left(2x+1\right)+7x^2\left(2x+1\right)+4x\left(2x+1\right)+\left(2x+1\right)\)
\(=\left(2x+1\right)\left(3x^4+6x^3+7x^2+4x+1\right)\)
\(=\left(2x+1\right)\left[\left(3x^4+3x^3+x^2\right)+\left(3x^3+3x^2+x\right)+\left(3x^2+3x+1\right)\right]\)
\(=\left(2x+1\right)\left[x^2\left(3x^2+3x+1\right)+x\left(3x^2+3x+1\right)+\left(3x^2+3x+1\right)\right]\)
\(=\left(2x+1\right)\left(3x^2+3x+1\right)\left(x^2+x+1\right)\)
e)
- Câu này có thể áp dụng định lý: nếu tổng các hệ số biến bậc chẵn và tổng các hệ số biến bậc lẻ bằng nhau thì đa thức có nhân tử x + 1.
- Nhận thấy: 1 + 4 + 4 + 1 = 3 + 4 + 3
\(x^6+3x^5+4x^4+4x^3+4x^2+3x+1\)
\(=(x^6+x^5)+(2x^5+2x^4)+(2x^4+2x^3)+(2x^3+2x^2)+(2x^2+2x)+(x+1)\)
\(=x^5(x+1)+2x^4(x+1)+2x^3(x+1)+2x^2(x+1)+2x(x+1)+(x+1)\)
\(=(x+1)(x^5+2x^4+2x^3+2x^2+2x+1)\)
Tiếp tục phân tích bằng cách trên vì 1 + 2 + 2 = 2 + 2 +1
\(=\left(x+1\right)\left(x+1\right)\left(x^4+x^3+x^2+x+1\right)\)
\(=\left(x+1\right)^2\left(x^4+x^3+x^2+x+1\right)\)
a) Gọi CT ghi hóa trị của NH3 là \(N^xH^I_3\) (x: nguyên, dương)
Theo quy tắc hóa trị, ta có:
\(x.1=I.3\\ =>x=\dfrac{1.I}{3}=III\)
Vậy: Hóa trị của N có hóa trị III trong hợp chất NH3
b) Gọi CT kèm hóa trị của Zn(OH)2 là \(Zn^x\left(OH\right)^y_2\) (x,y: nguyên, dương).
Theo quy tắc hóa trị, ta có:
\(x.1=y.2\\ =>\dfrac{x}{y}=\dfrac{2}{1}=\dfrac{II}{I}\)
=> x=II
y=I
=> Hóa trị của Zn là II trong hợp chất trên
tìm x,y
a) ( 3x-2)^3 - (3x - 2) ( 9x^2 + 6x +4) = 6( 3x+5)(5 - 3x )
b) ( 2x - 1)( 4x^2 - 4x +1) - (2x+ 1)^3+ 3(2x+5)(2x - 5)= -5
tìm x
1) (3x-2)(9x^2+6x+4)-(2x-5)(2x+5)=(3x-1)^3-(2x+3)^2+9x(3x-1)
2) (2x+1)^3-(3x+2)^2=(2x-5)(4x^2+10x+25)+6x(2x+1)-9x^2
P)(9-x)(x^2+2x-3) n)(-x+3)(x^2+x+1) O)(-6x+1/2)(x^2-4x+2) q)(6x+1)(x^2-2x-3) r)(2x+1)(-x^2-3x+1) U)(2x-3)(-x^2+x+6) s)(-4x+5)(x^2+3x-2) V)(-1/2x+3)(2x+6-4x^3)
p) \(\left(9-x\right)\left(x^2+2x-3\right)\)
\(=9\left(x^2+2x-3\right)-x\left(x^2+2x-3\right)\)
\(=9x^2+18x-27-x^3-2x^2+3x\)
\(=-x^3+7x^2+21x-27\)
n) \(\left(-x+3\right)\left(x^2+x+1\right)\)
\(=-x\left(x^2+x+1\right)+3\left(x^2+x+1\right)\)
\(=-x^3-x^2-x+3x^2+3x+3\)
\(=-x^2+2x^2+2x+3\)
o) \(\left(-6x+\dfrac{1}{2}\right)\left(x^2-4x+2\right)\)
\(=-6x\left(x^2-4x+2\right)+\dfrac{1}{2}\left(x^2-4x+2\right)\)
\(=-6x^3+24x^2-12x+\dfrac{1}{2}x^2-2x+1\)
\(=-6x^3+\dfrac{49}{2}x^2-14x+1\)
q) \(\left(6x+1\right)\left(x^2-2x-3\right)\)
\(=6x\left(x^2-2x-3\right)+\left(x^2-2x-3\right)\)
\(=6x^3-12x^2-18x+x^2-2x-3\)
\(=6x^3-11x^2-20x-3\)
r) \(\left(2x+1\right)\left(-x^2-3x+1\right)\)
\(=2x\left(-x^2-3x+1\right)+\left(-x^2-3x+1\right)\)
\(=-2x^3-6x^2+2x-x^2-3x+1\)
\(=-2x^3-7x^2-x+1\)
u) \(\left(2x-3\right)\left(-x^2+x+6\right)\)
\(=2x\left(-x^2+x+6\right)-3\left(-x^2+x+6\right)\)
\(=-2x^3+2x^2+12x+3x^2-3x-18\)
\(=-2x^3+5x^2+9x-18\)
s) \(\left(-4x+5\right)\left(x^2+3x-2\right)\)
\(=-4x\left(x^2+3x-2\right)+5\left(x^2+3x-2\right)\)
\(=-4x^3-12x^2+8x+5x^2+15x-10\)
\(=-4x^3-7x^2+23x-10\)
v) \(\left(-\dfrac{1}{2}x+3\right)\left(2x+6-4x^3\right)\)
\(=-\dfrac{1}{2}x\left(2x+6-4x^3\right)+3\left(2x+6-4x^3\right)\)
\(=-x^2-3+2x^4+6x+18-12x^3\)
\(=2x^4-12x^3-x^2+6x+15\)
p: (-x+9)(x^2+2x-3)
=-x^3-2x^2+3x+9x^2+18x-27
=-x^3+7x^2+21x-27
n: (-x+3)(x^2+x+1)
=-x^3-x^2-x+3x^2+3x+3
=-x^3+2x^2+2x+3
o: (-6x+1/2)(x^2-4x+2)
=-6x^3+24x^2-12x+1/2x^2-2x+1
=-64x^3+49/2x^2-14x+1
q: (6x+1)(x^2-2x-3)
=6x^3-12x^2-18x+x^2-2x-3
=6x^3-11x^2-20x-3
r: (2x+1)(-x^2-3x+1)
=-2x^3-6x^2+2x-x^2-3x+1
=-2x^3-7x^2-x+1
u: =-2x^3+2x^2+12x+3x^2-3x-18
=-2x^3+5x^2+9x-18
s: =-4x^3-12x^2+8x+5x^2+15x-10
=-4x^3-7x^2+23x-10
a. (2x + 5)(2x - 5)
b. (x2 + 3)(3 - x2 )
c. 3x(x -1)2 - 2x(x + 3)(x - 3) + 4x(x - 4)
d. 3x(4x - 3) - (2x -1)(6x + 5)
e. 4x(3x2 - x) - (2x + 3)(6x2 - 3x + 1)
f. (x - 2)(1x + 2)(x + 4)
\(\left(x^2+3\right)\left(3-x^2\right)\)
\(\left(x^2+3\right)\left(-x^2+3\right)\)
\(\left(-x^2+3\right).x^2+3\left(-x^2+3\right)\)
\(-x^2.x^2+3x^2+3\left(-x^2+3\right)\)
\(-x^2.x^2+3x^2-3x^2+9\)
\(-x^2.x^2+9\)
\(\left(2x+5\right)\left(2x-5\right)\)
\(2x\left(2x-5\right)+5\left(2x-5\right)\)
\(4x^2-10x+5\left(2x-5\right)\)
\(4x^2-10x+10x-25\)
\(4x^2-25\)