\(81x^2-6yz-9y^2-z^2\)

\(=\left(9x\right)^2-\left(6yz+9y^2+z^2\right)\)

\(=\left(9x\right)^2-\left(z+3y\right)^2\)

\(=\left(9x-z-3y\right)\left(9x+z+3y\right)\)

đề đúng chứ bạn????????

\(=81x^2-\left(z+3y\right)^2\)

\(=\left(9x+z+3y\right)\left(9x-z-3y\right)\)

a, \(6x^3y^2.\left(2-x\right)+9x^2y^2\left(x-2\right)\)
\(=6x^3y^2.\left(2-x\right)-9x^2y^2\left(2-x\right)\)
\(=y^2.\left(2-x\right)\left(6x^3-9x^2\right)\)
\(=3x^2y^2.\left(2-x\right)\left(2x-3\right)\)

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

a. x⁴+2= (x⁴+\(2\sqrt{2}x^2+2\)) - \(2\sqrt{2}x^2^{ }\) = 

\(\left(x^2+\sqrt{2}\right)^2-2\sqrt{2}x^2=\left(x^2-\sqrt{2\sqrt{2}}x+\sqrt{2}\right)\left(x^2+2\sqrt{2}x+\sqrt{2}\right)\)b. 81x²-(9y²+6yz+z²)=81x² - (3y+z)²=(9x-3y-z)(9x+3y+z)

a)\(81x^2-6yz-9y^2-z^2\)

\(=81x^2-\left(z-3y\right)^2\)

\(=\left(9x-z+3y\right)\left(9x+z-3y\right)\)

b)\(x^2y-x^3-9y+9x\)

\(=x^2\left(y-x\right)-9\left(y-x\right)\)

\(=\left(y-x\right)\left(x-3\right)\left(x+3\right)\)

c)\(3a^2-6ab+3b^2-12c^2\)

\(=3\left(a^2-2ab+b^2-4z^2\right)\)

\(=3\left[\left(a-b\right)^2-4z^2\right]\)

\(=3\left(a-b-2z\right)\left(a-b+2z\right)\)

a)\(81x^2-6yz-9y^2-z^2=\left(9x\right)^2-\left(9y^2+6yz+z^2\right)=\left(9x\right)^2-\left(3y+z\right)^2=\left(9x-3y-z\right)\left(9x+3y+z\right)\)b)\(x^2y-x^3-9y+9x=x^2\left(y-x\right)-9\left(y-x\right)=\left(x^2-9\right)\left(y-x\right)=\left(x-3\right)\left(x+3\right)\left(y-x\right)\)

c)\(3a^2-6ab+3b^2-12c^2=3\left(a^2-2ab+b^2-4c^2\right)=3\left[\left(a-b\right)^2-\left(2c\right)^2\right]=3\left(a-b-2c\right)\left(a-b+2c\right)\)

a) = x² (y - x) - 9( y - x) = ( y - x ) ( x² - 9) = ( y -x) ( x - 3 ) ( x + 3)

b) = x² ( x - 1 ) - 16 ( x - 1 ) = ( x - 1 ) ( x² - 16 ) = ( x - 1 ) ( x - 4 ) ( x + 4 )

c) = (9x)² - ( 9y² + 6yz + z² ) = (9x)² - ( 3y + z)² = (9x - 3y - z ) ( 9x + 3y + z)

d) = z( x - y) - ( x² -2xy + y² ) = z(x - y) - (x - y)² = (x - y) (z - 1)

e) = (x + 3) (x + 5)

f) = (x - 4) ( x + 3)

g) = (9x)² + 2.9x.2 + 2² - 36x = (9x + 2)² - (\(6\sqrt{x}\))² = \(\left(9x+2+6\sqrt{x}\right)\). \(\left(9x+2-6\sqrt{x}\right)\)

a) x²y - x³ - 9y + 9x = x²(y - x) - 9(y - x) = (y - x)(x² - 9) = (y - x)(x + 3)(x - 3).

b) x²(x - 1) + 16(1 - x) = (x - 1)(x² - 16) = (x - 1)(x - 4)(x + 4).

c) 81x² - 6yz - 9y² - z² = (9x)² - ((3y)² + 2.3yz + z²) = (9x)² - (3y + z)² = (9x + 3y +z)(9x - 3y - z).

d) xz - yz - x² + 2xy - y² = z(x - y) - (x - y)² = (x - y)(z - x + y).

e) x² + 8x + 15 = (x² + 3x) + (5x + 15) = x(x + 3) + 5(x + 3) = (x + 3)(x + 5).

f) x² - x - 12 = (x² - 4x) + (3x - 12) = x(x - 4) + 3(x - 4) = (x - 4)(x + 3).

g) (Đề sai) 81x⁴ + 4 = (81x⁴ + 36x² + 4) - 36x² = (9x² + 2)² - 36x² = (9x² + 2 + 6x)(9x² + 2 - 6x).

Ờ hé quên mất \(-\left(36x\right)=-\left(6\sqrt{x}\right)^2\)

a) Ta có: \(x^2-25+y^2+2xy\)

\(=\left(x^2+2xy+y^2\right)-25\)

\(=\left(x+y\right)^2-5^2\)

\(=\left(x+y-5\right)\left(x+y+5\right)\)

c) Ta có: \(3x^2-6xy+3y^2\)

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

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

d) Ta có: \(2x^2+2y^2-x^2z+z-y^2z-2\)

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

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

e) Ta có: \(x^2-2xy+y^2-16\)

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

\(=\left(x-y-4\right)\left(x-y+4\right)\)

\(81x^2-6yz-9y^2-z^2=81x^2-\left(6yz+9y^2+z^2\right)\)

\(=81x^2-\left(9y^2+6xy+z^2\right)=81x^2-\left(3y+z\right)^2\)

\(=\left(9x-3y-z\right)\left(9x+3y+z\right)\)

a) Ta có : x² - y² - 2x + 2y

= (x² - y²) - (2x - 2y)

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

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

a, x² - y² - 2x + 2y

= ( x² - y² ) - ( 2x - 2y )

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

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

b)2x +2y -x^2 -xy

= 2. ( x + y ) - x.( x + y )

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