\(12x^2y^3-10x^2y^3:5x^2y^2+4xy\left(1-3xy\right)^2\)

\(=12x^2y^3-2y+4xy\left(1-6xy+9x^2y^2\right)\)

\(=12x^2y^3-2y+4xy-24x^2y^2+36x^3y^3\)

\(x^3-y^3-36xy\)

\(=\left(x-y\right)^3+3xy\left(x-y\right)-36xy\)

\(=12^3+36xy-36xy\)

\(=1728\)

a, 12x²y - 6xy = 6xy . (2x - 1)

b, x³ - 2x² + x = x. (x² - 2x + 1) = x . (x - 1)²

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

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

\(=2x^3y-6x^2y^2+6x^2y^2-18xy^3\)

\(=2x^3y-18xy^3\)

b) \(\left(6x^5y^2-9x^4y^3+15x^3y^4\right):3x^3y^2\)

\(=6x^5y^2:3x^3y^2-9x^4y^3:3x^3y^2+15x^3y^4:3x^3y^2\)

\(=2x^2-3xy+5y^2\)

c) \(\left(2x+3\right)^2+\left(2x+5\right)^2-2\left(2x+3\right)\left(2x+5\right)\)

\(=\left(2x+3-2x-5\right)^2\)

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

d) \(\left(y+3\right)^3-\left(3-y\right)^2-54y\)

\(=y^3+9y^2+27y+27-\left(x^2-6x+9\right)-54y\)

\(=y^3+9y^2-27y+27-x^2+6y-9\)

\(=y^3+9y^2-x^2-21y+18\)

thay n đặt A

A=n^5-n

=n(n^4-1)

=n(n-1)(n+1)(n^2+1)n(n-1)(n+1) chia hết cho 6

nếu n=5k => A chia hết cho 5.6=30

nếu n=5k+1 => -1 chia hết cho 5 => A chia hết cho 30

Nếu n=5k+2 => ^2+1=25k^2+20k+5 chia hết cho 5

=> A chia hết cho 10nếu n=5k+3 =>^2+1=25k^2+30k+10 chia hết cho 5

=>A chia hết cho 30

Nếu n=5k+4 =>+1=5k+5 chia hết cho 5

=>A chia hết cho 30

Vậy với n nguyên dương thì n^5-n chia hết cho 30

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

xog a

tốt

Bài làm

a) 3x² - 6x² + 3x

= -3x² + 3x

= 3x( 1 - x )

b) 3x² + 5x - 3xy - 5y

= ( 3x² - 3xy ) + ( 5x - 5y )

= 3x( x - y ) + 5( x - y )

= ( x - y )( 3x + 5 )

c) x³ + 2x² + x

= x( x² + 2x + 1 )

= x( x² + 2.x.1 + 1² )

= x( x + 1 )²

d) xy + y² - x - y

= ( xy - x ) + ( y² - y )

= x( y - 1 ) + y( y - 1 )

= ( y - 1 )( x +  y )

# Học tốt #