`1,`

Cách 1: Chứng minh theo hằng đẳng thức

`(x-1)(x^2+x+1)=x^3-1^3=x^3-1`

Cách 2: Chứng minh theo tích chất phân phối

`(x-1)(x^2+x+1)=x(x^2+x+1)-(x^2+x+1)=x^3+x^2+x-x^2-x-1=x^3-1`

........

`2,` Xem lại đề

\(1,=461\times\left(42+58\right)=461\times100=46100\\ 2,=396\times\left(37-17\right)=396\times20=7920\)

a,C1 
 (5/6 + 5/8) x 2/3
= 35/24 x 2/3
=35/36
C2
 (5/6 + 5/8) x 2/3
= 5/6x2/3 + 5/8x2/3
= 10/18 + 10/24
= 35/36

b,C1
7/5 x 3/4 - 1/2 x 3/4
= 21/20 - 3/8
= 27/40
C2
7/5 x 3/4 - 1/2 x 3/4
=3/4 x (7/5-1/2)
=3/4x9/10
=27/40

a, 5/6 x (1/8x2/3) 

=5/6 x 1/12

=5/72

b,(7/5 - 1/2) x 3/4 

=0,9 x 3/4

=3,06

c,(5/6+5/8) x 2/3

=70/48 x 2/3

=35/36

a, 5/6 x (1/8x2/3) 

=5/6 x 1/12

=5/72

b,(7/5 - 1/2) x 3/4 

=0,9 x 3/4

=3,06

c,(5/6+5/8) x 2/3

=70/48 x 2/3

=35/36

a: =5/6(1/8+2/3)=5/6*19/24=95/144

b: =3/4(7/5-1/2)=27/40

c: =35/24*2/3=35/36

a: =5/48+10/18=95/144

b: =3/4(7/5-1/2)=3/4x9/10=27/40

c: =2/3x35/24=70/72=35/36

a) C1

 \(\dfrac{1}{8}\times\dfrac{5}{6}+\dfrac{5}{6}\times\dfrac{2}{3}=\dfrac{5}{6}\times\left(\dfrac{1}{8}+\dfrac{2}{3}\right)=\dfrac{5}{6}\times\dfrac{19}{24}=\dfrac{95}{144}\)

   C2

\(\dfrac{1}{8}\times\dfrac{5}{6}+\dfrac{5}{6}\times\dfrac{2}{3}=\dfrac{5}{48}+\dfrac{10}{18}=\dfrac{95}{144}\)

b) C1

  \(\dfrac{7}{5}\times\dfrac{3}{4}-\dfrac{1}{2}\times\dfrac{3}{4}=\dfrac{3}{4}\times\left(\dfrac{7}{5}-\dfrac{1}{2}\right)=\dfrac{3}{4}\times\dfrac{9}{10}=\dfrac{27}{40}\)

    C2 

   \(\dfrac{7}{5}\times\dfrac{3}{4}-\dfrac{1}{2}\times\dfrac{3}{4}=\dfrac{21}{20}-\dfrac{3}{8}=\dfrac{27}{40}\)

c) C1

 \(\left(\dfrac{5}{6}+\dfrac{5}{8}\right)\times\dfrac{2}{3}=\dfrac{35}{24}\times\dfrac{2}{3}=\dfrac{35}{36}\)

  C2 

  \(\left(\dfrac{5}{6}+\dfrac{5}{8}\right)\times\dfrac{2}{3}=\left(\dfrac{5}{6}\times\dfrac{2}{3}\right)+\left(\dfrac{5}{8}\times\dfrac{2}{3}\right)=\dfrac{5}{9}+\dfrac{5}{12}=\dfrac{35}{36}\)

\(=\dfrac{14+15}{18}\cdot\dfrac{3}{5}=\dfrac{29}{18}\cdot\dfrac{3}{5}=\dfrac{29}{30}\)