Trả lời:

7x² - 7y² - 14x + 14y 

= 7 ( x² - y² - 2x + 2y )

= 7 [ ( x² - y² ) - ( 2x - 2y ) ] 

= 7 [ ( x - y )( x + y ) - 2 ( x - y ) ]

= 7 ( x - y )( x + y - 2 )

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

xy - y^2 - x + y 

= y ( x - y ) - ( x - y ) 

= ( x - y ) ( y - 1 ) 

5x² - 20 = 5( x² - 4 ) = 5( x - 2 )( x + 2 )

5x^2 - 20 

= 5 ( x^2 - 4 ) 

= 5 ( x^2 - 2^2 ) 

= 5 ( x - 2 ) ( x + 2 ) 

x(x-y) + y(y-x)

= x(x-y) - y (x-y)

=(x-y)(x-y)

=(x-y)²

Thay x =56; y =7 vào ta được:

(56 -7)² = 49² =2401

Vậy giá trị của biểu thức là 2401 khi x = 56; y=7

Trả lời:

34, x⁶ + 1 = (x²)³ + 1³ = ( x²  + 1 )( x⁴ + x² + 1 )

35, x⁶ - y⁶ = (x³)² - (y³)² = ( x³ - y³ )( x³ + y³ ) = ( x - y )( x² + xy + y² )( x + y )( x² - xy + y² )

36, x¹² - y⁴ = (x⁶)² - (y²)² = ( x⁶ - y² )( x⁶ + y² ) = [ (x³)² - y² ]( x⁶ + y² ) = ( x³ - y )( x³ + y )( x⁶ + y² )

37, 1/27 + a³ = (1/3)³ + a³ = ( 1/3 + a )( 1/9 + 1/3a + a² )

38, 1/8x³ - 8 = (1/2a)³ - 2³ = ( 1/2a - 2 )( 1/4a² + a + 4 )

39, 27 - 27m + 9m² - m³ = 3³ - 3.3².m + 3.3.m² - m³ = ( 3 - m )³

40, \(125-\left(x+2\right)^2=\left(5\sqrt{5}\right)^2-\left(x+2\right)^2=\left(5\sqrt{5}-x-2\right)\left(5\sqrt{5}+x+2\right)\)

a) \(x^2-2x-5=0\)

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

\(\Leftrightarrow\left(x-1\right)^2=6\)

\(\Leftrightarrow x=1\pm\sqrt{6}\)

b) \(x^2-3x-1=0\)

\(\Leftrightarrow x^2-3x+\frac{9}{4}=\frac{13}{4}\)

\(\Leftrightarrow\left(x-\frac{3}{2}\right)^2=\frac{13}{4}\)

\(\Leftrightarrow x=\frac{3\pm\sqrt{13}}{2}\)

c) \(x^4-4x^2+3=0\)

\(\Leftrightarrow x^4-4x^2+4=1\)

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

\(\Leftrightarrow\orbr{\begin{cases}x^2-2=1\\x^2-2=-1\end{cases}}\)

\(\Leftrightarrow\orbr{\begin{cases}x=\pm\sqrt{3}\\x=\pm1\end{cases}}\)

d) \(x^2+xy+y^2=0\)

\(\Leftrightarrow x^2+xy+\frac{1}{4}y^2+\frac{3}{4}y^2=0\)

\(\Leftrightarrow\left(x+\frac{1}{2}y\right)^2+\frac{3}{4}y^2=0\)

\(\Leftrightarrow\hept{\begin{cases}x+\frac{1}{2}y=0\\y=0\end{cases}}\)

\(\Leftrightarrow x=y=0\).