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a) 4a2b3 - 6a3b2 = 2a2b2( 2b - 3a )
b) ( a - b )2 - ( b - a ) = ( a - b )2 + ( a - b ) = ( a - b )( a - b + 1 )
c) ( 8a3 - 27b3 ) - 2a( 4a2 - 9b2 ) = 8a3 - 27b3 - 8a3 + 18ab2 = 18ab2 - 27b3 = 9b2( 2a - 3b )
d) 10x2 + 10xy + 5x + 5y = 10x( x + y ) + 5( x + y ) = ( x + y )( 10x + 5 ) = 5( x + y )( 2x + 1 )
e) 5ay - 3bx + ax - 15by = 5y( a - 3b ) + x( a - 3b ) = ( a - 3b )( 5y + x )
a) \(4a^2.b^3-6a^3.b^2=2a^2.b^2\left(2b-3a\right)\)
b) \(\left(a-b\right)^2-\left(b-a\right)=\left(a-b\right)^2+\left(a-b\right)\)
\(=\left(a-b\right).\left(a-b+1\right)\)
c) \(8a^3-27b^3-2a.\left(4a^2-9b^2\right)=8a^3-27b^3-8a^3+18ab^2\)
\(=-27b^3+18ab^2=18ab^2-27b^3=9b^2.\left(2a-3b\right)\)
d) \(10x^2+10xy+5x+5y=5.\left(2x^2+2xy+x+y\right)\)
\(=5.\left[\left(2x^2+2xy\right)+\left(x+y\right)\right]=5.\left[2x\left(x+y\right)+\left(x+y\right)\right]\)
\(=5\left(x+y\right)\left(2y+1\right)\)
e) \(5ay-3bx+ax-15by=\left(5ay-15by\right)-\left(3bx-ax\right)\)
\(=5y\left(a-3b\right)-x\left(3b-a\right)=5y\left(a-3b\right)+x\left(a-3b\right)\)
\(=\left(a-3b\right)\left(x+5y\right)\)
Câu 2 nha
\(a,x^4+2x^3+x^2\)
\(=x^2\left(x^2+2x+1\right)\)
\(=x^2\left(x+1\right)^2\)
\(c,x^2-x+3x^2y+3xy^2+y^3-y\)
\(=\left(x^3+3x^2y+3xy^2+y^3\right)-\left(x+y\right)\)
\(=\left(x+y\right)^3-\left(x+y\right)\)
\(=\left(x+y\right)\left(x^2+2xy+y^2-1\right)\)
a) 5ay - 3bx + ax - 15by
= (5ay + ax) - (3bx + 15by)
= a (5y + x) - 3b (x + 5y)
= (5y + x) (a - 3b)
b) x^3 + x^2 - x - 1
= (x^3 + x^2) - (x + 1)
= x^2 (x + 1) - (x + 1)
= (x + 1) (x^2 - 1)
c) (2a + b)^2 - (2b + a)^2
= 4a^2 + 4ab + b^2 - 4b^2 - 4ab - a^2
= 3a^2 - 3b^2
= 3 (a^2 - b^2)
d) (8a^3 - 27b^3) - 2a (4a^2 - 9b^2)
= 8a^3 - 27b^3 - 8a^3 + 18ab^2
= 27b^3 + 18ab^2
= 9b^2 (3b + 2a)
5x2 - 10xy + 5y2 - 20z2
= 5.(x2 - 2xy + y2 - 4z2)
= 5.[(x2 - 2xy + y2) - (2z)2]
= 5.[(x - y)2 - (2z)2]
= 5.(x - y - 2z).(x - y + 2z)
x2.(1 - x2) - 4 + 4x2
= x2.(1 - x2) - 4.(1 - x2)
= (1 - x2).(x2 - 4)
= (1 - x)(1 + x)(x - 2)(x + 2)
5x2 - 10xy + 5y2 - 20z2
= 5.(x2 - 2xy + y2 - 4z2)
= 5.[(x2 - 2xy + y2) - (2z)2]
= 5.[(x - y)2 - (2z)2]
= 5.(x - y - 2z).(x - y + 2z)
x2.(1 - x2) - 4 + 4x2
= x2.(1 - x2) - 4.(1 - x2)
= (1 - x2).(x2 - 4)
= (1 - x)(1 + x)(x - 2)(x + 2)
\(a,x\left(x^2+4x+4\right)=x\left(x+2\right)^2\)
\(b,x\left(y+1\right)+y+1=\left(x+1\right)\left(y+1\right)\)
\(c,\left(x+y\right)^2-9z^2=\left(x+y-3z\right)\left(x+y+3z\right)\)
\(d,5\left(x^2-2x+1-y^2\right)=5\left(\left(x+1\right)^2-y^2\right)=5\left(x+1-y\right)\left(x+1+y\right)\)
a, 8x2+10x =2x.(4x+5)
b, 4x2-8x+4 =4.(x2 -2x+1)=4.(x-1)2
c, 3x2 -3xy -5x +5y =(3x2-5x) - (3xy-5y) = x.(3x-5)- y.(3x-5)= (x-y).(3x-5)
d, x2+ 4x- 45=x2+ 9x- 5x- 45= x.(x+9)- 5.(x+9)=(x-5).(x+9)
a , 8 x 2 + 10 x
= 2 x ( 4 x + 5 )
b , 4 x 2 - 8 x + 4
= ( 2x ) 2 - 2 . 2 x . 2 + 2 2
= ( 2x + 2 ) 2
c ) 3 x 2 - 3 x y - 5 x + 5 y
= 3 x ( x - y ) - 5 ( x - y )
= ( 3x - 5 ) ( x - y )
d ) x 2 + 4x - 45
= x 2 + 2 x . 2 + 4 - 49
= ( x + 2 ) 2 - 49
= ( x + 2 ) 2 - 7 2
= ( x + 2 - 7 ) ( x + 2 + 7)
= ( x - 5 ) ( x + 9 )
\(10x^2+10xy+5x+5y\)
\(=\left(10x^2+10xy\right)+\left(5x+5y\right)\)
\(=10x\left(x+y\right)+5\left(x+y\right)\)
\(=\left(10x+5\right)\left(x+y\right)\)
\(=5\left(5x+1\right)\left(x+y\right)\)