a: \(=\dfrac{5}{7}\left(\dfrac{5}{11}+\dfrac{2}{11}-\dfrac{14}{11}\right)=\dfrac{5}{7}\cdot\dfrac{-7}{11}=-\dfrac{5}{11}\)

b: \(=\dfrac{12}{7}\left(19+\dfrac{5}{8}-15-\dfrac{1}{4}\right)=\dfrac{12}{7}\cdot\left(4+\dfrac{3}{8}\right)\)

\(=\dfrac{12}{7}\cdot\dfrac{35}{8}=\dfrac{3}{2}\cdot5=\dfrac{15}{2}\)

c: \(=\dfrac{2}{15}-\dfrac{2}{15}\cdot5+\dfrac{3}{15}=\dfrac{2}{15}\cdot\left(-4\right)+\dfrac{3}{15}=\dfrac{-8+3}{15}=\dfrac{-5}{15}=-\dfrac{1}{3}\)

d: \(=\dfrac{4}{9}\left(19+\dfrac{1}{3}-39-\dfrac{1}{3}\right)=\dfrac{4}{9}\cdot\left(-20\right)=-\dfrac{80}{9}\)

a) xy + x + 8y + 8

= x.(y + 1) + 8.(y + 1)

= (y + 1).(x + 8)

b) \(x^2-x-\frac{2}{3}.x+\frac{2}{3}\)

\(=x.\left(x-1\right)-\frac{2}{3}.\left(x-1\right)\)

\(=\left(x-1\right).\left(x-\frac{2}{3}\right)\)

c) x² - 1

= x² + x - x - 1

= x.(x + 1) - (x + 1)

= (x + 1).(x - 1)

a) (xy+x) +(8y+8)=x(y+1)+8(y+1)=(x+8)(y+1)

b) (x²-x) -(2/3x-2/3)=x(x-1)+2/3(x-1)=(x+2/3)(x-1)

c) x²-1= (x-1)(x+1)

\(x^2-1=\left(x+1\right)\left(x-1\right)\)(Nhớ k cho mình với nhé!)

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

x² - 1 = x² - x + x - 1 = x . (x - 1) + (x - 1) = (x - 1) . (x + 1)

\(a,10.a^6+20a^5=10a^5\left(a+2\right)\)

\(b,5x^2-10xy+5y^2=5\left(x^2-2xy+y^2\right)=5\left(x-y\right)^2\)

\(c,3ab^3+6ab^2-18ab=3ab\left(b^2+2b-1\right)\)

\(d,15x^3y^2+10x^2y^2-20x^2y^3=5x^2y^2\left(3x+2-4y\right)\)

\(e,a^2\left(x-1\right)-b\left(1-x\right)=a^2\left(x-1\right)+b\left(x-1\right)=\left(x-1\right)\left(a^2+b\right)\)

\(f,x\left(x-5\right)-4\left(5-x\right)=x\left(x-5\right)+4\left(x-5\right)=\left(x-5\right)\left(x+4\right)\)

(mk sửa lại thứ tự là a,b,c,d,e,f nha)

chúc bn học tốt

\(1,10a^6+20a^5=10a^5\left(a+10\right)\)

\(2,5x^2-10xy+5y^2=5\left(x^2-2xy+y^2\right)\)

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

\(3,3ab^3+6ab^2-18ab\)

\(=3ab\left(b^2+2b-6\right)\)

\(4,15x^3y^2+10x^2y^2-20x^2y^3\)

\(=5x^2y^2\left(3x+2-4y\right)\)

\(5,a^2\left(x-1\right)-b\left(1-x\right)\)

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

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

\(6,x\left(x-5\right)-4\left(5-x\right)\)

\(=x\left(x-5\right)+4\left(x-5\right)\)

\(=\left(x+4\right)\left(x-5\right)\)

mk sửa lại câu 3 chút nha
\(3ab^3+6ab^2-18ab=3ab\left(b^2+2b-6\right)\)

xl vì sai sót
chúc bn học tốt nhé

\(a\left(x-1\right)+b\left(1-x\right)=a\left(x-1\right)-b\left(x-1\right)=\left(x-1\right)\left(a-b\right)\)

a) ( x + 1) + b ( 1 - x )

= ( x + 1 ) - b( x-   1 )

= ( 1 - b )( x- 1 )

**** 

a(x-1) + b(1-x)

= a(x-1) - b(x-1)

= (a-b)(x-1)

Nhấn đúng cho mk nha!!!!!!!!!

1) 5⁵ - 5⁴ + 5³ = 5³ . 5² - 5³ . 5 - 5³

= 5³ . ( 5² - 5 + 1 )

= 5³ . ( 25 - 5 - 1 )

= 5³ . 21

= 5³ . 3 . 7 chia hết cho 7

Vậy chứng minh 5⁵ - 5⁴ + 5³ chia hết cho7

2) 7⁶ + 7⁵ - 7⁴ = 7⁴ . 7² + 7⁴ . 7 - 7⁴

= 7⁴ . ( 7² + 7 - 1 )

= 7⁴ . ( 49 + 7 - 1 )

= 7⁴ . 55

= 7⁴ . 5 .11 chia hết cho 11

Vậy chứng minh 7⁶ + 7⁵ - 7⁴ chia hết cho 11

Tích mình nha !!!!!!!!!!!!!!!!!

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

a, y(x+1+8+8)

y(x+17)

b, x(x-1)

a) xy + x + 8y + 8

= x ( y + 1 ) + 8 ( y + 1 )

= ( y + 1 ) . ( x + 8 )

b) x² - 1  

= x² - x + x - 1 

= x ( x - 1 ) + ( x - 1 )

= ( x - 1 ) . ( x + 1 )

\(S=2\left(1+2\right)+2^3\left(1+2\right)+...+2^{11}\left(1+2\right)=3\left(2+2^3+...+2^{11}\right)⋮3\)

\(S=2\left(1+2+2^2\right)+...+2^{10}\left(1+2+2^2\right)=7\left(2+...+2^{10}\right)⋮7\)

Vì S chia hết cho 2 và S chia hết cho 3 

nên \(S⋮6\)