\(a,\left(2x-16\right)^7=128\\ \Rightarrow\left(2x-16\right)^7=2^7\\ \Rightarrow2x-16=2\\ \Rightarrow2x=18\\ \Rightarrow x=9\\ b,x^3.x^2=2^8:2^3\\ \Rightarrow x^5=2^5\\ \Rightarrow x=5\\ c,3^{x-3}-3^2=2.3^2\\ \Rightarrow3^{x-3}-9=18\\ \Rightarrow3^{x-3}=27\\ \Rightarrow3^{x-3}=3^3\\ \Rightarrow x-3=3\\ \Rightarrow x=6\)

Bài 1: 

c: x=4

b: x=2

a) (x - 140) : 7 = 3³ - 2³ . 3

(x - 140) : 7 = 27 - 8 . 3 = 27 - 24 = 3

x - 140 = 3 x 7 = 21

x = 21 + 140 = 161

b) x³ . x² = 2⁸ : 2³

x⁵ = 2⁵

=> x = 2

c) (x + 2) . ( x - 4) = 0

x = -2 hoặc 4

d) 3^x-3 - 3² = 2 . 3² =

3^x-3 - 9 = 2 . 9 = 18

3^x-3 = 18 + 9 = 27

3^x-3 = 3³

=> x - 3 = 3

x = 3 + 3 = 6

2.

a) 9 : ( x + 2 )

9 ⋮ 1 ; 9 ⋮ 3 ; 9 ⋮ 9

=> x = -1 ; 1 ; 7

a) \(=x^3\left(x-1\right)-\left(x-1\right)=\left(x-1\right)\left(x^3-1\right)\)

\(=\left(x-1\right)^2\left(x^2+x+1\right)\)

b) \(=xy\left(x+y\right)-\left(x+y\right)=\left(x+y\right)\left(xy-1\right)\)

c) Đổi đề: \(a^2x+a^2y-7x-7y\)

\(=a^2\left(x+y\right)-7\left(x+y\right)=\left(x+y\right)\left(a^2-7\right)\)

d) \(=x^2\left(a-b\right)+y\left(a-b\right)=\left(a-b\right)\left(x^2+y\right)\)

e) \(=x^3\left(x+1\right)+\left(x+1\right)=\left(x+1\right)\left(x^3+1\right)\)

\(=\left(x+1\right)^2\left(x^2-x+1\right)\)

g) \(=\left(x-y\right)^2-z\left(x-y\right)=\left(x-y\right)\left(x-y-z\right)\)

h) \(=\left(x-y\right)\left(x+y\right)+\left(x+y\right)=\left(x+y\right)\left(x-y+1\right)\)

i) \(=\left(x+1\right)^2-4=\left(x+1-2\right)\left(x+1+2\right)=\left(x-1\right)\left(x+3\right)\)

a\(x^3\left(x-1\right)-\left(x-1\right)=\left(x-1\right)\left(x^3-1\right)\)

b)\(=xy\left(x+y\right)-\left(x+y\right)=\left(x+y\right)\left(xy-1\right)\)

d)\(=a\left(x^2+y\right)-b\left(x^2+y\right)=\left(x^2+y\right)\left(x-b\right)\)

e)\(=x^3\left(x+1\right)+\left(x+1\right)=\left(x+1\right)\left(x^3+1\right)\)

g)\(=\left(x-y\right)^2-z\left(x-y\right)=\left(x-y\right)\left(x-y-z\right)\)

h)\(=\left(x-y\right)\left(x+y\right)-\left(x-y\right)=\left(x-y\right)\left(x+y-1\right)\)

i)\(=\left(x-1\right)^2-4=\left(x-1-2\right)\left(x-1+2\right)=\left(x-3\right)\left(x+1\right)\)

3: \(x^3+3x^2-16x-48\)

\(=x^2\left(x+3\right)-16\left(x+3\right)\)

\(=\left(x+3\right)\left(x-4\right)\left(x+4\right)\)

Bài 5

a) A = -x³ + 6x² - 12x + 8

= -x³ + 3.(-x)².2 - 3.x.2² + 2³

= (-x + 2)³

= (2 - x)³

Thay x = -28 vào A ta được:

A = [2 - (-28)]³

= 30³

= 27000

b) B = 8x³ + 12x² + 6x + 1

= (2x)³ + 3.(2x)².1 + 3.2x.1² + 1³

= (2x + 1)³

Thay x = 1/2 vào B ta được:

B = (2.1/2 + 1)³

= 2³

= 8

Bài 6

a) 11³ - 1 = 11³ - 1³

= (11 - 1)(11² + 11.1 + 1²)

= 10.(121 + 11 + 1)

= 10.133

= 1330

b) Đặt B =  x³ - y³ = (x - y)(x² + xy + y²)

= (x - y)(x² - 2xy + y² + 3xy)

= (x - y)[(x - y)² + 3xy]

Thay x - y = 6 và xy = 9 vào B ta được:

B = 6.(6² + 3.9)

= 6.(36 + 27)

= 6.63

= 378

Bài 6 :

a) \(11^3-1=\left(11-1\right)\left(11^2+11+1^2\right)\)

\(\)\(=10.\left(121+12\right)\)

\(=10.133\)

\(=1330\)

b) \(\left\{{}\begin{matrix}x-y=6\\xy=9\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}x^2+y^2-2xy=36\\xy=9\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}x^2+y^2-2.18=36\\xy=9\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}x^2+y^2=72\\xy=9\end{matrix}\right.\)

Ta có :

\(x^3-y^3=\left(x-y\right)\left(x^2+y^2+xy\right)\)

\(=6.\left(72+9\right)\)

\(=6.81\)

\(=486\)

\(\left(\dfrac{1}{15}+\dfrac{1}{35}+\dfrac{1}{63}\right)x=1\)

\(\Leftrightarrow\dfrac{1}{9}x=1\)

\(\Leftrightarrow x=1:\dfrac{1}{9}\)

\(\Leftrightarrow x=9\)

=>1/2(2/15+2/35+2/63)*x=1

=>1/2(1/3-1/5+1/5-1/7+1/7-1/9)*x=1

=>1/2*2/9*x=1

=>x*1/9=1

=>x=9

a) \(A=-x^3+6x^2-12x+8\)

\(A=-\left(x^3-6x^2+12x-8\right)\)

\(A=-\left(x-2\right)^3\) 

Thay x=-28 vào A ta có:

\(A=-\left(-28-2\right)^3=27000\)

Vậy: ...

b) \(B=8x^3+12x^2+6x+1\)

\(B=\left(2x\right)^3+3\cdot\left(2x\right)^2\cdot1+3\cdot2x\cdot1^2+1^3\)

\(B=\left(2x+1\right)^3\)

Thay \(x=\dfrac{1}{2}\) vào B ta có:
\(B=\left(2\cdot\dfrac{1}{2}+1\right)^3=8\)

Vậy: ...

1) A=1/8; 2) B=9472; 3) 0 và 10.

1: \(A=2x^3y^4-5x\cdot x^2y^4+xy^2\cdot x^2y^2=-2x^3y^4=-2\cdot\left(-1\right)^3\cdot\dfrac{1}{16}=\dfrac{1}{8}\)

2: \(B=9x^4y^6\cdot\left(-4xy\right)+19x^3y^5\cdot\left(-2\right)x^2y^2\)

\(=-36x^5y^7-38x^5y^7\)

\(=-74x^5y^7=-74\cdot\left(-1\right)^5\cdot2^7=9472\)

3: \(f\left(-1\right)=3\cdot\left(-1\right)^4+7\cdot\left(-1\right)^3+4\cdot\left(-1\right)^2-2\cdot\left(-1\right)-2=0\)

\(f\left(1\right)=3+7+4-2-2=10\)