Đề đúng k bạn

a) = 9x² - ( y² - 10y + 25y² ) = ( 3x )² - ( y - 5 )² = ( 3x - y + 5 )( 3x + y - 5 )

b) = ( x³ - 8 ) - ( x² - 4x + 4 ) = ( x - 2 )( x² + 2x + 4 ) - ( x - 2 )² = ( x - 2 )( x² + x + 6 ) 

c) = ( 4a² - 4a + 1 ) - ( b² - 2bc + c² ) = ( 2a - 1 )² - ( b - c )² = ( 2a - b + c - 1 )( 2a + b - c - 1 )

d) = ( a³ + 3a² + 3a + 1 ) - 27b³ = ( a + 1 )³ - ( 3b )³ = ( a - 3b + 1 )( a² + 9b² + 3ab + 3b )

a. \(9x^2-\left(y^2-10y+25\right)=9x^2-\left(y-5\right)^2=\left(3x-y+5\right)\left(3x+y-5\right)\)

b.\(x^3-8-x^2+4x-4=\left(x-2\right)\left(x^2+2x+4\right)-\left(x-2\right)^2=\left(x-2\right)\left(x^2+x+6\right)\)

c.\(\left(4a^2-4a+1\right)-\left(b^2-2bc+c^2\right)=\left(2a-1\right)^2-\left(b-c\right)^2=\left(2a-1+b-c\right)\left(2a-1-b+c\right)\)

d.\(\left(a^3+3a^2+3a+1\right)-27b^3=\left(a+1\right)^3-\left(3b\right)^3=\left(a+1-3b\right)\left[\left(a+1\right)^2+3b\left(a+1\right)+9b^2\right]\)

\(B=9x^2+25y^2-6x+10y-7\)

\(B=\left(9x^2-6x+1\right)+\left(25y^2+10y+1\right)-9\)

\(B=\left(3x-1\right)^2+\left(5y+1\right)^2-9\ge-9\)

Vậy GTNN của B là -9 khi x = \(\frac{1}{3}\); y = \(-\frac{1}{5}\)

a) \(6x^2y+9+x^4y^2=\left(x^2y+3\right)^2\)

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

c) \(25y^4-10y^2+1=\left(5y^2-1\right)^2\)

\(a,=\left(x^2y+3\right)^2\\ b,=\left(2x+y\right)^2\\ c,=\left(5y^2-1\right)^2\)

a) a^2 (x-y) +y-x

  = a^2 (x-y) -(x-y)

  = (x-y) (a^2 -1)

  = (x-y)(a-1)(a+1)

b) m^2 -25y^2+10y -1

= m^2 -(25y^2 -10y +1)

= m^2-(5y-1)^2

=(m-5y+1)(m+5y-1)

c)  a^2 -4x^2 +8x -4

= a^2 -(4x^2 -8x+4)

=a^2 -( 2x-2)^2

=(a-2x+2)(a+2x-2)