21(x-y)²-7(y-x)³ 

=21(x²-y²)-7(y²-x²)

=21x²-21y²-7y²+7x²

=28x²-28y²

=28(x²-y²)

\(1,\\ a,=4\left(x-2\right)^2+y\left(x-2\right)=\left(4x-8+y\right)\left(x-2\right)\\ b,=3a^2\left(x-y\right)+ab\left(x-y\right)=a\left(3a+b\right)\left(x-y\right)\\ 2,\\ a,=\left(x-y\right)\left[x\left(x-y\right)^2-y-y^2\right]\\ =\left(x-y\right)\left(x^3-2x^2y+xy^2-y-y^2\right)\\ b,=2ax^2\left(x+3\right)+6a\left(x+3\right)\\ =2a\left(x^2+3\right)\left(x+3\right)\\ 3,\\ a,=xy\left(x-y\right)-3\left(x-y\right)=\left(xy-3\right)\left(x-y\right)\\ b,Sửa:3ax^2+3bx^2+ax+bx+5a+5b\\ =3x^2\left(a+b\right)+x\left(a+b\right)+5\left(a+b\right)\\ =\left(3x^2+x+5\right)\left(a+b\right)\\ 4,\\ A=\left(b+3\right)\left(a-b\right)\\ A=\left(1997+3\right)\left(2003-1997\right)=2000\cdot6=12000\\ 5,\\ a,\Leftrightarrow\left(x-2017\right)\left(8x-2\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x=2017\\x=\dfrac{1}{4}\end{matrix}\right.\\ b,\Leftrightarrow\left(x-1\right)\left(x^2-16\right)=0\Leftrightarrow\left[{}\begin{matrix}x=1\\x=4\\x=-4\end{matrix}\right.\)

A) 1/2 x(x^2-4)+4(x+2)

=1/2x(x-2)(x+2)+4(x+2)

=(x+2)(1/2x^2-x+4)

b) 21(x-y)^2-7(x-y)^3

= (x-y)^2(21-7x+7y)

=(x-y)^2.7(3-x+y)

c) 1/8x^3-3/4x^2+3/2x-1

=(1/2x)^3-3.(1/2x)^2.1+3.1/2x.1^2-1

=(1/2x-1)^3

\(9\left(x+5\right)^2-\left(x-7\right)^2\)

\(=\left(3x+15\right)^2-\left(x-7\right)^2\)

\(=\left(3x+15-x+7\right)\left(3x+15+x-7\right)\)

\(=\left(2x+22\right)\left(4x+8\right)\)

\(=2\left(x+11\right).4\left(x+2\right)\)

\(=8\left(x+11\right)\left(x+2\right)\)

x³ - 3x²y + 3xy² - y³ - z³

= (x³ - 3x²y + 3xy² - y³) - z³

= (x - y)³ - z³

= (x - y - z)[(x - y)² + (x - y)z + z²]

= (x - y - z)(x² - 2xy + y² + xz - yz + z³)

--------------------

x² - y² + 8x + 6y + 7

= (x² + 8x + 16) - (y² - 6y + 9)

= (x + 4)² - (y - 3)²

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

= (x - y + 7)(x + y + 1)

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

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

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

\(=\left(x-y-z\right)\left(x^2-2xy+y^2+xz-yz+z^2\right)\)

b: \(=x^2+8x+16-y^2+6y-9\)

=(x+4)^2-(y-3)^2

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

=(x+y+1)(x-y+7)

a) \(x^2-xy+x-y\)

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

\(=\left(x+1\right)\left(x-y\right)\)

b) \(x^2+5x+6\)

\(=x^2+2x+3x+6\)

\(=x\left(x+2\right)+3\left(x+2\right)\)

\(=\left(x+3\right)\left(x+2\right)\)

\(2xy-x^2-y^2+16\)

\(=16-\left(x-y\right)^2\)

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

a) \(14\left(x-y\right)^2+21\left(y-x\right)\)

\(=14\left(x-y\right)^2-21\left(x-y\right)\)

\(=7\left(x-y\right)\left[2\left(x-y\right)-3\right]\)

\(=7\left(x-y\right)\left(2x-2y-3\right)\)

b) \(7x^5\left(y-3\right)-49x^4\left(3-y\right)^3\)

\(=7x^4\left(y-3\right)\left[x+7\left(y-3\right)^2\right]\)

\(=7x^4\left(y-3\right)\left(x+7y^2-42y+63\right)\)

c) \(\left(x^2-9\right)^2-x^2\left(x-3\right)^2\)

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

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

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

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

d) \(\left(4x^2-1\right)^2-9\left(2x-1\right)^2\)

\(=\left(2x-1\right)^2\left(2x+1\right)^2-9\left(2x-1\right)^2\)

\(=\left(2x-1\right)^2\left[\left(2x+1\right)^2-9\right]\)

\(=\left(2x-1\right)^2\left(4x^2+4x+1-9\right)\)

\(=4\left(2x-1\right)^2\left(x^2+x-2\right)\)

\(=4\left(2x-1\right)^2\left(x-1\right)\left(x+2\right)\)

a) 14( x - y )² + 21( y - x )

= 14( x - y )² - 21( x - y )

= ( x - y )[ 14( x - y ) - 21 ]

= ( x - y )( 14x - 14y - 21 )

= 7( x - y )( 2x - 2y - 3 )

b) 7x⁵( y - 3 ) - 49x⁴( 3 - y )³

= 7x⁵( y - 3 ) + 49x⁴( y - 3 )³

= 7x⁴( y - 3 )[ x + 7( y - 3 )² ]

= 7x⁴( y - 3 )( x +7( y² - 6y + 9 ) ]

= 7x⁴( y - 3 )( x + 7y² - 42y + 63 )

c) ( x² - 9 )² - x²( x - 3 )²

= [ ( x - 3 )( x + 3 ) ]² - x²( x - 3 )²

= ( x - 3 )²( x + 3 )² - x²( x - 3 )²

= ( x - 3 )²[ ( x + 3 )² - x² ]

= ( x - 3 )²[ x² + 6x + 9 - x² ]

= ( x - 3 )²( 6x + 9 )

= 3( x - 3 )²( 2x + 3 )

d) ( 4x² - 1 )² - 9( 2x - 1 )²

= [ ( 2x - 1 )( 2x + 1 ) ]² - 9( 2x - 1 )²

= ( 2x - 1 )²( 2x + 1 )² - 9( 2x - 1 )²

= ( 2x - 1 )²[ ( 2x + 1 )² - 9 ]

= ( 2x - 1 )²( 4x² + 4x + 1 - 9 )

= ( 2x - 1 )²( 4x² + 4x - 8 )

= 4( 2x - 1 )²( x² + x - 2 )

= 4( 2x - 1 )²( x² - x + 2x - 2 )

= 4( 2x - 1 )²[ x( x - 1 ) + 2( x - 1 ) ]

= 4( 2x - 1 )²( x - 1 )( x + 2 )

=(x^3-y^3)-(x^2-y^2)

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

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

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

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

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

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

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

a, Thay x = -2 và  y = 1 vào BT, ta được:

\(M=5.\left(-2\right)^2.1+3.\left(-2\right).1-21=20-6-21=-7\)

b, Ta có: \(a^2-a-6=a^2-3a+2a-6=a\left(a-3\right)+2\left(a-3\right)=\left(a-3\right)\left(a+2\right)\)

a) Thay x=-2 và y=1 vào M, ta được:

\(M=5\cdot\left(-2\right)^2\cdot1+3\cdot\left(-2\right)\cdot1-21\)

\(=5\cdot4-3\cdot2-21\)

\(=20-6-21=14-21=-7\)

b) Ta có: \(a^2-a-6\)

\(=a^2-3a+2a-6\)

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

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

B(2y + z) (4 x - 7 y)

B nha

B