Câu 1: 

a: =>-2x-x+17=34+x-25

=>-3x+17=x+9

=>-4x=-8

hay x=2

b: =>17x+16x+27=2x+43

=>33x+27=2x+43

=>31x=16

hay x=16/31

c: =>-2x-3x+51=34+2x-50

=>-5x+51=2x-16

=>-7x=-67

hay x=67/7

e: 3x-32>-5x+1

=>8x>33

hay x>33/8

17x + 3. ( -16x – 37) = 2x + 43 - 4x

<=>17x-48x-111=-2x+43

<=>-29x=154

<=> \(x=-\frac{154}{29}\)

-3. (2x + 5) -16 < -4. (3 – 2x)

\(\Leftrightarrow-6x-31< -12+8x.\)

\(\Leftrightarrow-14x< 19\Rightarrow x< -\frac{19}{14}\)

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bài 1 tính giá trị biểu thức

( - 25 ) nhân ( -3 ) nhân x với x = 4

\(\left(-25\right).\left(-3\right).4\)

\(=\left(-25\right).4.\left(-3\right)\)

\(=-100.\left(-3\right)=300\)

( -1 ) nhân ( -4 ) nhân 5 nhân 8 nhân y với y =25

\(\left(-1\right).\left(-4\right).5.8.25\)

\(=4.5.8.25=4.25.5.8\)

\(=100.40=40000\)

( 2ab mũ 2 ) : c với a =4 ; b= -6 ; c =12

\(\left(2.4.\left(-6\right)\right)^2:12\)

\(=\left(-48\right)^2:12\)

\(=2304:12=192\)

[ ( -25 ) nhân ( - 27 ) nhân ( -x ) ] : y với x = 4 ; y = -9

\(\left[\left(-25\right).\left(-27\right).\left(-4\right)\right]:-9\)

\(=-2700:\left(-9\right)\)

\(=300\)

(a mũ 2 _ b mũ 2) : ( a + b ) nhân ( a _ b ) với a + 5 , b = -3

\(\left(5^2-\left(-3\right)^2\right):\left(5-3\right).\left(5+3\right)\)

\(=16:2.8\)

\(=8.8=64\)

bài 2 tìm x

( 2x _ 5 ) + 17 = 6

\(2x-5=-11\)

\(2x=-6\)

\(x=-3\)

10 _ 2 ( 4 _ 3x ) = - 4

\(2.\left(4-3x\right)=14\)

\(4-3x=7\)

\(3x=-3\)

\(x=-1\)

- 12 + 3 ( -x + 7 ) = -18

\(3\left(-x+7\right)=-6\)

\(-x+7=-2\)

\(-x=-9\)

\(x=9\)

24 : ( 3x _ 2 ) = -3

\(3x-2=-8\)

\(3x=-6\)

\(x=-2\)

- 45 : 5 nhân ( -3 _ 2x ) = 3

\(5.\left(-3-2x\right)=-15\)

\(-3-2x=-3\)

\(2x=0\)

\(x=0\)

bài 5:

1: \(\dfrac{12x^3y^2}{18xy^5}=\dfrac{12x^3y^2:6xy^2}{18xy^5:6xy^2}=\dfrac{2x^2}{3y^3}\)

2: \(\dfrac{10xy-5x^2}{2x^2-8y^2}=\dfrac{5x\cdot2y-5x\cdot x}{2\left(x^2-4y^2\right)}\)

\(=\dfrac{5x\left(2y-x\right)}{-2\left(x+2y\right)\left(2y-x\right)}=\dfrac{-5x}{2\left(x+2y\right)}\)

3: \(\dfrac{x^2-xy-x+y}{x^2+xy-x-y}\)

\(=\dfrac{\left(x^2-xy\right)-\left(x-y\right)}{\left(x^2+xy\right)-\left(x+y\right)}\)

\(=\dfrac{x\left(x-y\right)-\left(x-y\right)}{x\left(x+y\right)-\left(x+y\right)}=\dfrac{\left(x-y\right)\left(x-1\right)}{\left(x+y\right)\left(x-1\right)}=\dfrac{x-y}{x+y}\)

4: \(\dfrac{\left(x+1\right)\left(x^2-2x+1\right)}{\left(6x^2-6\right)\left(x^3-1\right)}\)

\(=\dfrac{\left(x+1\right)\left(x-1\right)^2}{6\left(x^2-1\right)\left(x-1\right)\left(x^2+x+1\right)}\)

\(=\dfrac{\left(x+1\right)\left(x-1\right)}{6\left(x-1\right)\left(x+1\right)\cdot\left(x^2+x+1\right)}\)

\(=\dfrac{1}{6\left(x^2+x+1\right)}\)

5: \(\dfrac{2x^2-7x+3}{1-4x^2}\)

\(=-\dfrac{2x^2-7x+3}{4x^2-1}\)

\(=-\dfrac{2x^2-6x-x+3}{\left(2x-1\right)\left(2x+1\right)}\)

\(=-\dfrac{2x\left(x-3\right)-\left(x-3\right)}{\left(2x-1\right)\left(2x+1\right)}\)

\(=-\dfrac{\left(x-3\right)\left(2x-1\right)}{\left(2x-1\right)\left(2x+1\right)}=\dfrac{-x+3}{2x+1}\)

Bài 3:

1: \(9x^3-xy^2\)

\(=x\cdot9x^2-x\cdot y^2\)

\(=x\left(9x^2-y^2\right)\)

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

2: \(x^2-3xy-6x+18y\)

\(=\left(x^2-3xy\right)-\left(6x-18y\right)\)

\(=x\left(x-3y\right)-6\left(x-3y\right)\)

\(=\left(x-3y\right)\left(x-6\right)\)

3: \(x^2-3xy-6x+18y\)

\(=\left(x^2-3xy\right)-\left(6x-18y\right)\)

\(=x\left(x-3y\right)-6\left(x-3y\right)\)

\(=\left(x-3y\right)\left(x-6\right)\)

4: \(6xy-x^2+36-9y^2\)

\(=36-\left(x^2-6xy+9y^2\right)\)

\(=36-\left(x-3y\right)^2\)

\(=\left(6-x+3y\right)\left(6+x-3y\right)\)

5: \(x^4-6x^2+5\)

\(=x^4-x^2-5x^2+5\)

\(=x^2\left(x^2-1\right)-5\left(x^2-1\right)\)

\(=\left(x^2-5\right)\left(x^2-1\right)\)

\(=\left(x^2-5\right)\left(x-1\right)\left(x+1\right)\)

6: \(9x^2-6x-y^2+2y\)

\(=\left(9x^2-y^2\right)-\left(6x-2y\right)\)

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

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

a/ \(x^3+3x^2+3x+1+6=0\)

\(\Leftrightarrow\left(x+1\right)^3=-6\)

\(\Leftrightarrow x+1=-\sqrt[3]{6}\)

\(\Rightarrow x=-1-\sqrt[3]{6}\)

b/ \(16x^3-16x^2+4x^2+3x-7=0\)

\(\Leftrightarrow16x^2\left(x-1\right)+\left(x-1\right)\left(4x+7\right)=0\)

\(\Leftrightarrow\left(x-1\right)\left(16x^2+4x+7\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x=1\\16x^2+4x+7=0\left(vn\right)\end{matrix}\right.\)

\(A=27x^3-54x^2+36x-8+54x^2-6+4\)

\(=27x^3+36x-10\)

\(B=8x^3+36x^2+54x+27-2x^3-12x^2-24x-16\)

\(=6x^3+24x^2+30x+9\)

Áp dụng HĐT \(a^3-b^3=\left(a-b\right)^3+3ab\left(a-b\right)\)

\(M=\left(-2\right)^3+3\left(x+y-1\right)\left(x+y+1\right)\left(-2\right)+6\left(x+y\right)^2\)

\(=-8-6\left[\left(x+y\right)^2-1\right]+6\left(x+y\right)^2\)

\(=-2\)

9) \(\left(a+b\right)^3-\left(a-b\right)^3\)

\(=\left(a+b-a+b\right)\left[\left(a+b\right)^2+\left(a+b\right)\left(a-b\right)+\left(a-b\right)^2\right]\)

\(=b^2\left[a^2+2ab+b^2+a\left(a-b\right)+b\left(a-b\right)+a^2-2ab+b^2\right]\)

\(=b^2\left(a^2+2ab+b^2+a^2-ab+ab-b^2+a^2-2ab+b^2\right)\)

\(=b^2\left(3a^2+b^2\right)\)

10) \(\left(6x-1\right)^2-\left(3x+2\right)^2\)

\(=\left(6x-1-3x-2\right)\left(6x-1+3x+2\right)\)

\(=\left(3x-3\right)\left(9x+1\right)\)

11) \(x^2-4x^2y^2+y^2+2xy\)

\(=\left(x^2+2xy+y^2\right)-4x^2y^2\)

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

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

12) \(\left(x^2-25\right)^2-\left(x-5\right)^2\)

\(=\left(x^2-25-x+5\right)\left(x^2-25+x-5\right)\)

\(=\left(x^2-x-20\right)\left(x^2-30+x\right)\)

13) \(x^6-x^4+2x^3+2x^2\)

\(=x^6-x^4+2x^3+2x^2-1+1\)

\(=\left(x^6+2x^3+1\right)-\left(x^4-2x^2+1\right)\)

\(=\left[\left(x^3\right)^2+2x^3.1+1^2\right]-\left[\left(x^2\right)^2-2x^2.1+1^2\right]\)

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

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

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

1) \(\left(x+y\right)^2-25\)

\(=\left(x+y\right)^2-5^2\)

\(=\left(x+y-5\right)\left(x+y+5\right)\)

2) \(100-\left(3x-y\right)^2\)

\(=10^2-\left(3x-y\right)^2\)

\(=\left(10-3x+y\right)\left(10+3x-y\right)\)

3) \(64x^2-\left(8a+b\right)^2\)

\(=\left(8x\right)^2-\left(8a+b\right)^2\)

\(=\left(8x-8a-b\right)\left(8x+8a+b\right)\)

4) \(4a^2b^4-c^4d^2\)

\(=\left(2ab^2\right)^2-\left(c^2d\right)^2\)

\(=\left(2ab^2-c^2d\right)\left(2ab^2+c^2d\right)\)

5) Đề đúng ko vậy ạ?

6) \(16x^3+54y^3\)

\(=2\left(8x^3+27y^3\right)\)

\(=2\left[\left(2x\right)^3+\left(3y\right)^3\right]\)

\(=2\left(2x+3y\right)\left[\left(2x\right)^2-2x.3y+\left(3y\right)^2\right]\)

\(=2\left(2x+3y\right)\left(4x^2-6xy+9y^2\right)\)

7) \(8x^3-y^3\)

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

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

\(=\left(2x-y\right)\left(4x^2+2xy+y^2\right)\)

8) \(\left(a+b\right)^2-\left(2ab-b\right)^2\)

\(=\left(a+b-2ab+b\right)\left(a+b+2ab-b\right)\)

\(=\left(a+2b-2ab\right)\left(a+2ab\right)\)