Phá ngoặc (x+4)(x-1)
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(x + 2)(x + 3) = x(x + 3) + 2(x + 3) = x2 + 3x + 2x + 6 = x2 + 5x + 6
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Khi phá ngoặc của của đa thức f(x) ta sẽ được đa thức \(f\left(x\right)=a_1x^n+a_2x^{n-1}+a_3x^{n-2}+...+a_{n-1}x+a_n\)(với n là bậc của đa thức)
Ta có:\(f\left(1\right)=a_1+a_2+a_3+...+a_{n-1}+a_n\)
Mà \(f\left(1\right)=\left(3-12+8\right)^{111}\cdot\left(4+3+2+1-12+1\right)^{2222}\)\(=-1\)
Suy ra:\(a_1+a_2+a_3+...+a_{n-1}+a_n=-1\)
Vậy tổng các hệ số của đa thức sau khi phá ngoặc là -1
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a) \(3x-10=2x+13\Leftrightarrow x=13+10=23\)
b) \(x+12=-5-x\Leftrightarrow2x=-17\Leftrightarrow x=-\frac{17}{2}\)
c) \(x+5=10-x\Leftrightarrow2x=5\Leftrightarrow x=\frac{5}{2}\)
d) \(6x+23=2x-12\Leftrightarrow4x=-35\Leftrightarrow x=-\frac{35}{4}\)
e) \(12-x=x+1\Leftrightarrow2x=11\Leftrightarrow x=\frac{11}{2}\)
f) \(14+4x=3x+20\Leftrightarrow x=20-14=6\)
g) \(2\left(x-1\right)+3\left(x-2\right)=x-4\Leftrightarrow2x-2+3x-6=x-4\)
\(\Leftrightarrow5x-8=x-4\Leftrightarrow4x=4\Leftrightarrow x=1\)
h ) \(3\left(4-x\right)-2\left(x-1\right)=x+20\Leftrightarrow12-3x-2x+2=x+20\)
\(\Leftrightarrow14-5x=x+20\Leftrightarrow6x=-6\Leftrightarrow x=-1\)
i ) \(4\left(2x+7\right)-3\left(3x-2\right)=24\Leftrightarrow8x+28-9x+6=24\)
\(\Leftrightarrow34-x=24\Leftrightarrow x=34-24=10\)
k) \(3\left(x-2\right)+2x=10\Leftrightarrow3x-6+2x=5x-6=10\)
\(\Leftrightarrow5x=10+6=16\Leftrightarrow x=\frac{16}{5}\)
Tự KL cho các phần
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a) \(3x-10=2x+13\)
\(\Leftrightarrow3x-2x=13+10\)
\(\Leftrightarrow x=23\)
b) \(x+12=-5-x\)
\(\Leftrightarrow x+x=-5-12\)
\(\Leftrightarrow2x=-17\)
\(\Leftrightarrow x=-\frac{17}{2}\)
c) \(x+5=10-x\)
\(\Leftrightarrow x+x=10-5\)
\(\Leftrightarrow2x=5\)
\(\Leftrightarrow x=\frac{5}{2}\)
d) \(6x+2^3=2x-12\)
\(\Leftrightarrow6x+8=2x-12\)
\(\Leftrightarrow6x-2x=-12-8\)
\(\Leftrightarrow4x=-20\)
\(\Leftrightarrow x=-5\)
e) \(12-x=x+1\)
\(\Leftrightarrow-x-x=1-12\)
\(\Leftrightarrow-2x=-11\)
\(\Leftrightarrow x=\frac{11}{2}\)
g) \(2\left(x-1\right)+3\left(x-2\right)=x-4\)
\(\Leftrightarrow2x-2+3x-6=x-4\)
\(\Leftrightarrow2x+3x-x=-4+6+2\)
\(\Leftrightarrow4x=4\)
\(\Leftrightarrow x=1\)
h) \(14+4x=3x+20\)
\(\Leftrightarrow4x-3x=20-14\)
\(\Leftrightarrow x=6\)
i) \(4\left(2x+7\right)-3\left(3x-2\right)=24\)
\(\Leftrightarrow8x+28-9x+6=24\)
\(\Leftrightarrow8x-9x=24-6-28\)
\(\Leftrightarrow-x=-10\)
\(\Leftrightarrow x=10\)
k) \(3\left(4-x\right)-2\left(x-1\right)=x+20\)
\(\Leftrightarrow12-3x-2x+2=x+20\)
\(\Leftrightarrow-3x-2x-x=20-2-12\)
\(\Leftrightarrow-6x=6\)
\(x=-1\)
l) \(3\left(x-2\right)+2x=10\)
\(\Leftrightarrow3x-6+2x=10\)
\(\Leftrightarrow3x+2x=10+6\)
\(\Leftrightarrow5x=16\)
\(\Leftrightarrow x=\frac{16}{5}\)
Lần sau bạn chỉ nên đăng ít câu hỏi một thôi nhé, đăng nnay các bạn làm không xuể đâu
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\(a.\left[\left(x+34\right)-50\right].2=56\\ \Leftrightarrow\left(x+34\right)-50=28\\ \Leftrightarrow x+34=78\\ \Rightarrow x=44\)
\(b.1045-\left[215-\left(3x-24\right)\right]=5\\ \Leftrightarrow215-\left(3x-24\right)=1040\\ \Leftrightarrow3x-24=-825\\ \Leftrightarrow3x=-801\\ \Rightarrow x=-267\)
\(c.\left[195-\left(15x-27\right)\right].39=4212\\ \Leftrightarrow195-\left(15x-27\right)=108\\ \Leftrightarrow15x-27=87\\ \Leftrightarrow15x=114\\ \Rightarrow x=7,6\)
a) [(x+34)] - 50] . 2 = 56
=x+34-50=56:2
=> x+34-50=28
->x=28+50-34
-> x=44
b,1045 - [ 215 - ( 3x - 24 )] = 5
1045-(215-3x+24)=5
1045-215+3x-24=5
1045-215-24-5=-3x
-> 801=-3x-> x=801:(-3)=-267
,c) [ 195 - ( 15x - 27)] . 39 = 4212
(195-15x+27).39=4212
(195-15x+27)=4212/39=108
195+27-108=15x
114=15x-> x=114/15=7,6
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`(1/4 + -5/13 ) + ( 2/11 +( -8/13) + 3/4 )`
`= 1/4 + -5/13 + 2/11 +( -8/13) + 3/4`
`=(1/4+3/4) + ( (-5)/13 + (-8)/13) + 2/11`
`= 1 + (-1)+2/11`
`=0+2/11`
`=2/11`
`(1/4+(-5)/13)+(2/11+(-8)/13+3/4)`
`=1/4+(-5)/13+2/11+(-8)/13+3/4`
`=(1/4+3/4)+( (-5)/13 + (-8)/13 ) + 2/11`
`= 1 + (-1) +2/11`
`= 0+2/11`
`=2/11`
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phá ngoặc đi bạn . thế này chưa là gì đâu :) mình ko thông minh thì mình chăm thôi
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(x+4)(x-1)=x.(x-1)+4.(x-1)
=(x^2-x)+4x-4
=x^2+3x-4
(x+4)(x-1)=x2-x+4x-4
= x2+3x-4