Câu 1: Ta có: A = \(x^3+y^3+3xy=x^3+y^3+3xy\times1=x^3+y^3+3xy\left(x+y\right)\)

\(=\left(x+y\right)^3=1^3=1\)

Câu 2: Ta có: \(B=x^3-y^3-3xy=\left(x-y\right)\left(x^2+xy+y^2\right)-3xy\)

\(=x^2+xy+y^2-3xy=x^2-2xy+y^2=\left(x-y\right)^2=1^2=1\)

Câu 3: Ta có: \(C=x^3+y^3+3xy\left(x^2+y^2\right)-6x^2.y^2\left(x+y\right)\)

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

\(=x^3+y^3+3xy\left(x+y\right)^2-3xy.2xy+6x^2y^2\)

\(=x^3+y^3+3xy.1-6x^2y^2+6x^2y^3\)

\(=x^3+y^3+3xy\left(x+y\right)=\left(x+y\right)^3=1^3=1\)

A

\(\frac{3}{5}\div\frac{4}{5}+\frac{1}{2}\times\frac{2}{3}\)

\(=\frac{3}{4}+\frac{1}{3}\)

\(=\frac{13}{12}\)

B

\(\frac{5}{4}\times x=\frac{3}{8}+\frac{1}{4}\)

 \(\frac{5}{4}\times x =\frac{5}{8}\)

\(x=\frac{5}{8}\div\frac{5}{4}\)

\(x=\frac{4}{8}=\frac{1}{2}\)

C1: \(A=\left(\frac{36}{6}-\frac{4}{6}+\frac{3}{6}\right)-\left(\frac{150}{30}+\frac{50}{30}-\frac{45}{30}\right)-\left(\frac{18}{6}-\frac{14}{6}+\frac{15}{6}\right)\)

\(=\frac{35}{6}-\frac{155}{30}-\frac{19}{6}=\frac{35}{6}-\frac{31}{6}-\frac{19}{6}=-\frac{15}{6}=-2\frac{1}{2}\)

C2: \(6-\frac{2}{3}+\frac{1}{2}-5-\frac{5}{3}+\frac{3}{2}-3+\frac{7}{3}-\frac{5}{2}\)

\(=\left(6-5-3\right)-\left(\frac{2}{3}+\frac{5}{3}-\frac{7}{3}\right)+\left(\frac{1}{2}+\frac{3}{2}-\frac{5}{2}\right)\)

\(=-2-0-\frac{1}{2}=-2\frac{1}{2}\)

giup minh voi cac ban

\(4+\frac{11}{8}-\frac{5}{6}=\frac{96+33-20}{24}=\frac{109}{24}\)

\(\left(\frac{1}{2}+\frac{4}{7}\right)-\left(\frac{3}{7}-\frac{3}{10}\right)=\frac{1}{2}+\frac{4}{7}-\frac{3}{7}+\frac{3}{10}\)

\(\left(\frac{1}{2}+\frac{3}{10}\right)+\left(\frac{4}{7}-\frac{3}{7}\right)=\frac{4}{5}+\frac{1}{7}=\frac{28+5}{35}=\frac{33}{35}\)

ban Chitanda Eru oi to bao nhung ma nhan voi bao nhieu ma ra duoc 96

       B = 1.2.3 + 2.3.4 + 3.4.5 + .... + 17.18.19 

<=> 4B = 1.2.3.4 + 2.3.4.4 + 3.4.5.4 + .... + 17.18.19.4 

<=> 4B = 1.2.3.(4 - 0) + 2.3.4.(5 - 1) + 3.4.5.(6 - 2) + .... + 17.18.19.(20 - 16)

<=> 4B = 1.2.3.4 + 2.3.4.5 - 1.2.3.4 + .... + 17.18.19.20 - 16.17.18.19

<=> 4B = 17.18.19.20 = 116280

<=> B = 116280 : 4 = 29070 

       B = 1.2.3 + 2.3.4 + 3.4.5 + .... + 17.18.19 

<=> 4B = 1.2.3.4 + 2.3.4.4 + 3.4.5.4 + .... + 17.18.19.4 

<=> 4B = 1.2.3.(4 - 0) + 2.3.4.(5 - 1) + 3.4.5.(6 - 2) + .... + 17.18.19.(20 - 16)

<=> 4B = 1.2.3.4 + 2.3.4.5 - 1.2.3.4 + .... + 17.18.19.20 - 16.17.18.19

<=> 4B = 17.18.19.20 = 116280

<=> B = 116280 : 4 = 29070 

( 2/3 x 1/5 + 1/5 ) : ( 2/3 : 1/5 - 1/5)     /     ( 1/2 - 21/47 )

= ( 2/5 + 1/5 ) : ( 10/3 - 1/5 )     /     ( 47/94 - 42/94 )

= ( 2/15 + 3/15 ) : ( 50/15 - 3/15 )     /     ( 5/94 )

=  1/3 : 47/15     /     5/94

= 15/141         /         5/94            ( Phép chia phân số thì nhân đảo ngược )

= 1410/705

= 2

( Dấu "gạch chéo" trước 1/2 là "phần" à? )

Ây lần sau thêm vài dấu ngoặc kép vào để rõ đề hơn nhé

mình gộp 2 ngoặc đơn đầu là tử số, phần sau / là mẫu số nhé.

b = ( 1+2-3-4) + ( 5+6-7-8) + .............. + (301+302-303-304) + (305 +305)

b = -4 + (-4) + ..................+ (-4) + 610

b= -4 x  76 + 610

b= -304 + 610

b= 306