1) Ta có: \(\left(\dfrac{3}{4}\cdot\dfrac{5}{97}+\dfrac{1}{9}\cdot\dfrac{13}{47}\right)\cdot\left(\dfrac{1}{5}-\dfrac{7}{25}\cdot\dfrac{5}{7}\right)\)

\(=\left(\dfrac{3}{4}\cdot\dfrac{5}{97}+\dfrac{1}{9}\cdot\dfrac{13}{47}\right)\cdot\left(\dfrac{1}{5}-\dfrac{1}{5}\right)\)

=0

2) Ta có: \(\dfrac{8}{17}\cdot\dfrac{4}{15}+\dfrac{8}{17}\cdot\dfrac{22}{15}-\dfrac{8}{15}\cdot\dfrac{9}{17}\)

\(=\dfrac{8}{17}\left(\dfrac{4}{15}+\dfrac{22}{15}-\dfrac{9}{15}\right)\)

\(=\dfrac{8}{17}\cdot\dfrac{15}{15}=\dfrac{8}{17}\)

3) Ta có: \(\dfrac{2021}{2}\cdot\dfrac{1}{3}+\dfrac{4042}{4}\cdot\dfrac{1}{5}+\dfrac{6063}{3}\cdot\dfrac{22}{15}\)

\(=\dfrac{2021}{2}\left(\dfrac{1}{3}+\dfrac{1}{5}\right)+2021\cdot\dfrac{22}{15}\)

\(=\dfrac{2021}{2}\cdot\dfrac{8}{15}+\dfrac{2021}{2}\cdot\dfrac{44}{15}\)

\(=\dfrac{2021}{2}\cdot\dfrac{52}{15}\)

\(=\dfrac{52546}{15}\)

4) Ta có: \(\dfrac{4}{7}\cdot\dfrac{2}{13}+\dfrac{8}{13}:\dfrac{7}{4}+\dfrac{4}{7}:\dfrac{13}{2}+\dfrac{4}{7}\cdot\dfrac{1}{13}\)

\(=\dfrac{4}{7}\left(\dfrac{2}{13}+\dfrac{8}{13}+\dfrac{2}{13}+\dfrac{1}{13}\right)\)

\(=\dfrac{4}{7}\)

1) Tính biểu thức:

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

\(x^4+2x^2-24=\left(x^2+6\right)\cdot\left(x^2-4\right)=\left(x-2\right)\left(x+2\right)\left(x^2+6\right)\)

1) 

=a^4+2a^2+1-a^2

=(a^2+1)^2-a^2

=(a^2-a+1)(a^2+a+1)

2)

=a^4+4b^4-4a^2b^2

=(a^2+2b^2)^2-4a^2b^2

=(a^2-2ab+2b^2)(a^2+2ab+2b^2)

3)

=(8x^2+1)^2-16x^2

=(8x^2-4x+1)(8x^2+4x+1).

4)

=x^5+x^4+x^3-x^3+1

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

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

5).

=x^7-x+x^2+x+1

=x(x^6-1)+x^2+x+1

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

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

=(x^2+x+1)[(x^2-x)(x^3+1)+1]

6)

=x^8-x^2+x^2+x+1

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

Xong nhóm x^2+x+1 vào.

7)

=x^4-(2x-1)^2

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

8)

=(a^8+b^8)^2-a^8b^8

=(a^8-a^4b^4+b^8)(a^8+a^4b^4+b^8).

Bạn nên viết đề bằng công thức toán và ghi đầy đủ yêu cầu đề để mọi người hiểu đề của bạn hơn nhé.

Bài 2: 

Ta có: \(\frac{x+1}{x}=10\) hay \(\frac{x^1+1^1}{x^1}=10^1\)

Nên suy ra : \(\frac{x^5+1}{x^5}=10^5\)

                                 = 100000 ( do 1⁵ cũng sẽ =1 nên không viết mũ 5 cũng chả sao)

a) \(x-\dfrac{3}{4}=6\times\dfrac{3}{8}\)

\(x-\dfrac{3}{4}=\dfrac{9}{4}\)

=> \(x=\dfrac{9}{4}+\dfrac{3}{4}=3\)

b) \(\dfrac{7}{8}:x=3-\dfrac{1}{2}\)

\(\dfrac{7}{8}:x=\dfrac{5}{2}\)

=> \(x=\dfrac{7}{8}:\dfrac{5}{2}=\dfrac{7}{20}\)

c) \(x+\dfrac{1}{2}\times\dfrac{1}{3}=\dfrac{3}{4}\)

\(x+\dfrac{1}{6}=\dfrac{3}{4}\)

=> \(x=\dfrac{3}{4}-\dfrac{1}{6}=\dfrac{7}{12}\)

d) \(\dfrac{3}{2}\times\dfrac{4}{5}-x=\dfrac{2}{3}\)

\(\dfrac{6}{5}-x=\dfrac{2}{3}\)

=> \(x=\dfrac{6}{5}-\dfrac{2}{3}=\dfrac{8}{15}\)

e) \(x\times3\dfrac{1}{3}=3\dfrac{1}{3}:4\dfrac{1}{4}\)(?)

\(x\times\dfrac{10}{3}=\dfrac{40}{51}\)

=> \(x=\dfrac{40}{51}:\dfrac{10}{3}=\dfrac{4}{17}\)

f) \(5\dfrac{2}{3}:x=3\dfrac{2}{3}-2\)

\(\dfrac{17}{3}:x=\dfrac{5}{3}\)

=> \(x=\dfrac{17}{3}:\dfrac{5}{3}=\dfrac{17}{5}\)

a: =>x-3/4=18/8=9/4

=>x=9/4+3/4=12/4=3

b: =>7/8:x=5/2

=>x=7/8:5/2=7/8*2/5=14/40=7/20

c: x+1/2*1/3=3/4

=>x+1/6=3/4

=>x=3/4-1/6=9/12-2/12=7/12

d: =>12/10-x=2/3

=>6/5-x=2/3

=>x=6/5-2/3=18/15-10/15=8/15

e: =>x*10/3=10/3:17/4=10/3*4/17

=>x=4/17

f: =>17/3:x=13/3-5/2=26/6-15/6=11/6

=>x=17/3:11/6=17/3*6/11=34/11

1, a⁴ + a² + 1 

= a⁴ + 2a² + 1 - a² 

= (a²)² + 2a² + 1 - a² 

= (a² + 1)² - a² 

= (a² + 1 - a)(a² + 1 + a)

2, a⁴ + 4b⁴ 

= (a²)² + 2. a² . b² + (2b)² - a² . b² 

= (a² + 2b)² - (ab)² 

= (a² + 2b - ab)(a² + 2b + ab)

3, 64x⁴ + 1 

= (8x²)²​ + 16x²​ + 1 - 16x²​ 

= (8x² + 1)²​ - (4x)²​ 

= (8x² + 1 - 4x)(8x² + 1 + 4x)

4, x⁵ + x⁴ + 1 

= x⁵ + x⁴ + x³ - x³ - x² - x + x + x² + 1 

= (x⁵ + x⁴ + x³) - (x³ + x² + x) + (x + x² + 1)

= x³(x² + x + 1) - x(x² + x + 1) + (x² + x + 1)

= (x² + x + 1)(x³ - x + 1)

5, x⁷ + x² + 1 

= x⁷ – x + x² + x + 1

= x(x⁶ – 1) + (x² + x + 1) 

= x(x³ – 1)(x³ + 1) + (x² + x + 1)

= x(x³ + 1)(x – 1) (x² + x + 1) + (x² + x + 1) 

= (x² + x + 1)[ x(x³ + 1)(x – 1) + 1]

= (x² + x + 1)(x⁵ – x⁴ + x³ – x² + x – 1)

6, x⁸ + x + 1 

= x⁸ + x⁷ + x⁶ - x⁷ - x⁶ - x⁵ + x⁵ + x⁴ + x³ - x⁴ - x³ - x² + x² + x + 1

= (x⁸ + x⁷ + x⁶) -  (x⁷ + x⁶ + x⁵) + (x⁵ + x⁴ + x³ ) - (x⁴ + x³ + x²) + (x² + x + 1)

= x⁶(x² + x + 1) - x⁵(x² + x + 1) + x³(x² + x + 1) - x²(x² + x + 1) + (x² + x + 1)

= (x² + x + 1)(x⁶ - x⁵ + x³ - x² + 1)

7, x⁴ - 4x² + 4x - 1 

= x⁴ - (4x² - 4x + 1)

= (x²)² - (2x - 1)²

= (x² - 2x + 1)(x² + 2x - 1)

= (x - 1)² (x² + 2x - 1)

8, a¹⁶ + a⁸b⁸ + b¹⁶

=  (a¹⁶ + 2a⁸b⁸ + b¹⁶) - a⁸b⁸ 

= (a⁸ + b⁸)² - (a⁴b⁴)²

= (a⁸ + b⁸ - a⁴b⁴)(a⁸ + b⁸ + a⁴b⁴)

= (a⁸ + b⁸ - a⁴b⁴)[(a⁸ + b⁸ + 2a⁴b⁴) - a⁴b⁴]

= (a⁸ + b⁸ - a⁴b⁴)[(a⁴ + b⁴)² - (a²b²)²]

= (a⁸ + b⁸ - a⁴b⁴)(a⁴ + b⁴ - a²b²)(a⁴ + b⁴ + a²b²)

= (a⁸ + b⁸ - a⁴b⁴)(a⁴ + b⁴ - a²b²)[(a⁴ + b⁴ + 2a²b²) - a²b²]

= (a⁸ + b⁸ - a⁴b⁴)(a⁴ + b⁴ - a²b²)[(a² + b²) - (ab)²]

= (a⁸ + b⁸ - a⁴b⁴)(a⁴ + b⁴ - a²b²)(a² + b² - ab)(a² + b² + ab)

a)\(=\dfrac{3}{3}+\dfrac{4}{3}=\dfrac{7}{3}\)

b)\(=\dfrac{5}{9}\times\dfrac{3}{2}=\dfrac{15}{18}=\dfrac{5}{6}\)

d)\(=\left(\dfrac{12}{8}-\dfrac{3}{8}\right)\times2=\dfrac{9}{8}\times2=\dfrac{18}{8}=\dfrac{9}{4}\)

c)\(=\dfrac{4}{3}-\dfrac{5}{6}=\dfrac{8}{6}-\dfrac{5}{6}=\dfrac{3}{6}=\dfrac{1}{2}\)

a) 1 + 4/3 = 7/3

b) 5/9 : 2/3 = 5/6

c ) 4/3 -1/3 x 5/2

= 1 x 5/2

= 5/2

d) ( 3/2 - 3/8) : 1/2

= 9/8 : 1/2

= 9/4

e) 15/16 : 3/8 x 3/4 

= 5/2 x 3/4

= 15/8

f) 7/19 x 1/3 x 7/19 x 2/3

= 7/19 x (1/3 x 2/3)

= 7/19 x 2/9

= 14/171

g) 3/5 x 8/27 x 25/3

= 3/5 x 25/3 x 8/27 

= 5 x 8/27

= 40/27

h) 1/5 + 4/11 + 4/5 + 7/11

= (1/5 + 4/5) + (4/11 + 7/11)

= 1 + 1

= 2

e)\(\dfrac{15}{16}\times\dfrac{8}{3}\times\dfrac{3}{4}=\dfrac{360}{192}=\dfrac{15}{8}\)

f) \(=\dfrac{7}{19}\times\left(\dfrac{1}{3}+\dfrac{2}{3}\right)=\dfrac{7}{19}\times\dfrac{3}{3}=\dfrac{7}{19}\)

g)\(=\dfrac{600}{120}=\dfrac{600:120}{120:120}=\dfrac{5}{1}=5\)

h)\(=\left(\dfrac{1}{5}+\dfrac{4}{5}\right)+\left(\dfrac{4}{11}+\dfrac{7}{11}\right)=\dfrac{5}{5}+\dfrac{11}{11}=1+1=2\)