Đáp án không thôi nhá chứ giải mất tg lắm

a) \(6x^2-8x=2x\left(3x-4\right)\)

b) \(21x^2y^7-12x^5y^3=3x^2y^3\left(7y^4-4x^3\right)\)

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

d) \(24x^2y-18xy^2=6xy\left(4x-3y\right)\)

e) \(9x^2y^2+12x^2y-15xy^2=3xy\left(3xy+4x-5y\right)\)

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

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

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

beautifully

excitedly

interesting

collected

arrangements

peacefully

excited

different

a,\(x^2-7x+6=x^2-x-6x+6\)

                       \(=x\left(x-1\right)-6\left(x-1\right)\)

                        \(=\left(x-6\right)\left(x-1\right)\)

a) x²-7x+6=(x²-x)-(6x-6)=x(x-1)-6(x-1)=(x-6)(x-1)

b) x²-6x+3=(x²-6x+9)-6=(x-3)²-\(\sqrt{6^2}\)=(x-3-\(\sqrt{6}\))(x-3+\(\sqrt{6}\))

c) x²-4x+3=(x²-x)-(3x-3)=x(x-1)-3(x-1)=(x-3)(x-1)

d) 3x²-5x+2=(3x²-3x)-(2x-2)=3x(x-1)-2(x-1)=(3x-2)(x-1)

e) 7x²-x-6=(7x²-7x)+(6x-6)=7x(x-1)+6(x-1)=(7x+6)(x-1)

f) 3x²-5x-8=(3x²+3x)-(8x+8)=3x(x+1)-8(x+1)=(3x-8)(x+1)

g) x²-6x+5=(x²-x)-(5x-5)=x(x-1)-5(x-1)=(x-5)(x-1)

h) x²-2x-3=(x²-2x+1)-4=(x-1)²-2²=(x-1-2)(x-1+2)=(x-3)(x+1)

i) x²-x-12=(x²+3x)-(4x+12)=x(x+3)-4(x+3)=(x-4)(x+3)

Lời giải:

ĐKĐB $\Rightarrow \frac{2}{c}=\frac{a+b}{ab}\Rightarrow c(a+b)=2ab$

Khi đó:

$\frac{a}{b}-\frac{a-c}{c-b}=\frac{a(c-b)-b(a-c)}{b(c-b)}=\frac{ac-ab-ab+bc}{b(c-b)}=\frac{c(a+b)-2ab}{b(c-b)}=\frac{2ab-2ab}{b(c-b)}=0$

$\Rightarrow \frac{a}{b}=\frac{a-c}{c-b}$ (đpcm) 

1 interested in travelling by plane

2 15 minutes riding his bike to school

3 is made by my mother everymorning

4 take care of her little brother

5 able to speak 2 languages when he was young

6 able to play the piano

7 is played all over VN

8 to play voleyball very well when he was young

9 to go fishing when he was young

10 way to the shopping mall

over

camping

was

couldn't

percussion

takes

look after

go around 

go through

wind

how long

for

do

1 does this red dress cost

2 is this shirt

does this short cost

3 do these shoes cost

4 has brown backpack

5 how to get to the bus stop

6 to stay in bed

7 are cleaned by Nga everyday

8 is played with a bow

9 worked for that company for 10 years

10 15 minutes walking to school

Bài cuối mình không thấy rõ đề nhưng mình đoán là thế này bạn nhé.

a.

$ax-ay+bx-by=(ax-ay)+(bx-by)=a(x-y)+b(x-y)$

$=(a+b)(x-y)$

b. Trùng phần a

c. 

$x^2+xy+ax+ay=(x^2+xy)+(ax+ay)=x(x+y)+a(x+y)$

$=(x+a)(x+y)$

d.

$x^2y+xy^2-x-y=(x^2y+xy^2)-(x+y)$

$=xy(x+y)-(x+y)=(xy-1)(x+y)$

e.

$x^2y-xy^2-5x+5y=(x^2y-xy^2)-(5x-5y)$

$=xy(x-y)-5(x-y)=(x-y)(xy-5)$

f. Biểu thức không phân tích được thành nhân tử

g.

$x^2y-4x+xy^2-4y$

$=(x^2y+xy^2)-(4x+4y)=xy(x+y)-4(x+y)=(x+y)(xy-4)$
h.

$x^4+x^3+x+1=(x^4+x^3)+(x+1)$
$=x^3(x+1)+(x+1)=(x^3+1)(x+1)=(x+1)(x^2-x+1)(x+1)$

$=(x+1)^2(x^2-x+1)$