Bài 2

a) A = (-2x²y² + 4xy - 6xy³) : 2xy

= -xy + 2 - 3y²

Thay x = 1/2; y = 4 vào A, ta có:

A = -1/2 . 4 + 2 - 3 . 2²

= -2 + 2 - 12

= -12

b) B = 25x² - 10xy² + y⁴

= (5x - y²)²

Thay x = 2; y = 3 vào B, ta có:

B = (5.2 - 3²)²

= (10 - 9)²

= 1²

= 1

c) C = (3x + 2)² + 2(3x + 2)(2y - 1)² + (2y - 1)²

= (3x + 2 + 2y - 1)²

= (3x + 2y + 1)²

Thay x = 1/3; y = -1/2 vào C, ta có:

C = [3 . 1/3 + 2 . (-1/2) + 1]²

= (1 - 1 + 1)²

= 1²

= 1

Bài 3

a) x³ + 2x² = x²(x + 2)

b) 3(x - y) - 5x(y - x)

= 3(x - y) + 5x(x - y)

= (x - y)(3 + 5x)

c) 4x³ - 9x

= x(4x² - 9)

= x(2x - 3)(2x + 3)

d) (x - 2y)² - 4(x + y)²

= (x - 2y)² - [2(x + y)]²

= (x - 2y) - (2x + 2y)²

= (x - 2y - 2x - 2y)(x - 2y + 2x + 2y)

= (-x - 4y).3x

= -3x(x + 4y)

e) x²y + x² - 4y - 4

= (x²y + x²) - (4y + 4)

= x²(y + 1) - 4(y + 1)

= (y + 1)(x² - 4)

= (y + 1)(x - 2)(x + 2)

f) -27x³(x + 1) + x + 1

= - 27x³(x + 1) + (x + 1)

= (x + 1)(-27x³ + 1)

= (x + 1)(1 - 27x³)

= (x + 1)(1 - 3x)(1 + 3x + 9x²)

b, 9a² - 6a + 1 - 25b²

= (3a - 1)² - (5b)²

= (3a - 1 - 5b).(3a -1 + 5b)

b,

B =  \(\dfrac{1}{x+2}\) + \(\dfrac{5}{x-2}\) - \(\dfrac{2x}{x^2-4}\) (đk \(x\) ≠ -2; 2)

B = \(\dfrac{1}{x+2}+\dfrac{5}{x-2}-\dfrac{2x}{\left(x-2\right)\left(x+2\right)}\)

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

B = \(\dfrac{x-2+5x+10-2x}{\left(x+2\right).\left(x-2\right)}\)

B = \(\dfrac{4x+8}{\left(x-2\right)\left(x+2\right)}\)

B = \(\dfrac{4}{x-2}\)

C,  

C = \(\dfrac{1}{x+1}\) + \(\dfrac{2}{1-x}\) - \(\dfrac{1-5x}{x^2-1}\) Đk \(x\ne\) -1; 1

C = \(\dfrac{x-1}{\left(x+1\right)\left(x-1\right)}\) - \(\dfrac{2.\left(x+1\right)}{\left(x-1\right)\left(x+1\right)}\) - \(\dfrac{1-5x}{\left(x-1\right)\left(x+1\right)}\)

C = \(\dfrac{x-1-2x-2-1+5x}{\left(x-1\right)\left(x+1\right)}\)

C = \(\dfrac{-4x-4}{\left(x+1\right)\left(x-1\right)}\)

C = \(\dfrac{-4\left(x+1\right)}{\left(x-1\right)\left(x+1\right)}\)

C = \(\dfrac{-4}{x-1}\)

Chọn B

Remarkable: đáng chú ý 

Have you ever been to Britain? I’ve dreamed of going there (1) __ I was a little girl and finally, (2) ___ the spring of 2012, it happened. I was there three weeks and (3) ___much of that time soaking up the culture, history, and scenery of this incredible island. I visited several districts in England, Wales and Scotland and even (4) ___ a site trip to Ireland. Every place I went to seemed to be more interesting and more beautiful (5) ____the last. The tour I was with began in London. Of all the sights I saw there, the Tower of London was the most (6) ___The Tower is a building complex of incredibly rich history.

Also on the Thames are the Houses of Parliament and, of course, the clock tower housing “Big Ben”. I saw so many landmarks I can hardly remember them all. Although it was just a glimpse of London I did, (7) __, get a chance to see all the (8)____ famous places.

After (9) ___ of days in London we traveled to the south of England stopping to visit Stonehenge. If you don’t know about Stonehenge there are a couple of links on my links page that will (10) ___ you to sites that can fill you in.

   1. A. for                        B. while                     C. since                      D. because

   2. A. on                         B. in                            C. at                            D. to

   3. A. spent                    B. took                       C. did                         D. used

   4. A. did                        B. got                          C. spent                      D. made

   5. A. then                      B. as                           C. with                       D. than

   6. A. interesting           B. interested              C. interest                  D. interestingly

   7. A. at first                  B. at all                      C. at least                   D. at that

   8. A. more                    B. much                     C. most                       D. many

   9. A. few                       B. some                      C. a couple                D. little

   10. A. reach                  B. take                        C. make                      D. send

a: ABCD là hình vuông

=>AC cắt BD tại trung điểm của mỗi đường

=>O là trung điểm chung của AC và BD

Gọi M là giao điểm của BF và AD

Xét ΔADB có

DE,AO là các đường trung tuyến

DE cắt AO tại F

Do đó: F là trọng tâm của ΔADB

Xét ΔADB có

F là trọng tâm

BF cắt AD tại M

Do đó: M là trung điểm của AD

Xét ΔMAB vuông tại A và ΔMDI vuông tại D có

MA=MD

\(\hat{AMB}=\hat{DMI}\) (hai góc đối đỉnh)

Do đó: ΔMAB=ΔMDI

=>AB=DI

mà AB=DC

nên DI=DC

=>D là trung điểm của IC

b: Xét tứ giác ABDI có

AB//DI

AB=DI

Do đó: ABDI là hình bình hành

\(\left(x-2\right)\left(x-5\right)=x\left(x-5\right)-2\left(x-5\right)\\ =x^2-5x-2x+10\\ =x^2-7x+10\)

cíu với

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