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a, x(a - b) + (a - b)
= (x + 1)(a - b)
b, x(a + b) - a - b
= x(a + b) - (a + b)
= (x - 1)(a + b)
c, 10ax - 5ay - 2x + y
= 5a(2x - y) - (2x - y)
= (5a - 1)(2x - y)
d, 2a^2x - 5by - 5a^2y + 2bx
= 2x(a^2 + b) - 5y(b + a^2)
= (2a - 5y)(a^2 + b)
làm tiếp:
2ax2 - bx2 - 2ax +bx +4a-2b
= x2(2a-b) - x(2a-b) +2(2a-b)
=(2a-b)(x2-x+2)
A = 4acx + 4bcx + 4ax + 4bx ( đã sửa '-' )
= 4x( ac + bc + a + b )
= 4x[ c( a + b ) + ( a + b ) ]
= 4x( a + b )( c + 1 )
B = ax - bx + cx - 3a + 3b - 3c
= x( a - b + c ) - 3( a - b + c )
= ( a - b + c )( x - 3 )
C = 2ax - bx + 3cx - 2a + b - 3c
= x( 2a - b + 3c ) - ( 2a - b + 3c )
= ( 2a - b + 3c )( x - 1 )
D = ax - bx - 2cx - 2a + 2b + 4c
= x( a - b - 2c ) - 2( a - b - 2c )
= ( a - b - 2c )( x - 2 )
E = 3ax2 + 3bx2 + ax + bx + 5a + 5b
= 3x2( a + b ) + x( a + b ) + 5( a + b )
= ( a + b )( 3x2 + x + 5 )
F = ax2 - bx2 - 2ax + 2bx - 3a + 3b
= x2( a - b ) - 2x( a - b ) - 3( a - b )
= ( a - b )( x2 - 2x - 3 )
= ( a - b )( x2 + x - 3x - 3 )
= ( a - b )[ x( x + 1 ) - 3( x + 1 ) ]
= ( a - b )( x + 1 )( x - 3 )
\(2ax-bx+3cx-2a+b-3c\\ =x\left(2a-b+3c\right)-\left(2a-b+3c\right)\\ =\left(x-1\right)\left(2a-b+3c\right)\)
\(ax-bx-2cx-2a+2b+4c\\ =x\left(a-b-2c\right)-2\left(a-b-2c\right)\\ =\left(x-2\right)\left(a-b-2c\right)\)
\(3ax^2+3bx^2+ax+bx+5a+5b\\ =3x^2\left(a+b\right)+x\left(a+b\right)+5\left(a+b\right)\\ =\left(3x^2+x+5\right)\left(a+b\right)\)
\(ax^2-bx^2-2ax+2bx-3a+3b\\ =x^2\left(a-b\right)-2x\left(a-b\right)-3\left(a+b\right)\\ =\left(x^2-2x-3\right)\left(a+b\right)\\ =\left(x+1\right)\left(x-3\right)\left(a+b\right)\)
\(ax^2-3axy+bx-3by\\ =x\left(ax+b\right)-3y\left(ax+b\right)\\ =\left(x-3y\right)\left(ax+b\right)\)
\(5x^2y+5xy^2-a^2x-a^2y\\ =5xy\left(x+y\right)-a^2\left(x+y\right)\\ =\left(5xy-a^2\right)\left(x+y\right)\)
\(2ax^3+6ax^2+6ax+18a\\ =2ax^2\left(x+3\right)+6a\left(x+3\right)\\ =2a\left(x^2+3\right)\left(x+3\right)\)
\(10xy^2-5by^2+2ax-ab\\ =5y^2\left(2x-b\right)+a\left(2x-b\right)\\ =\left(5y^2+a\right)\left(2x-b\right)\)
\(ax-bx+cx-3a+3b-3c\\ =x\left(a-b+c\right)-3\left(a-b+c\right)\\ =\left(x-3\right)\left(a-b+c\right)\)
5.
\(4x^5y^2+8x^4y^3+4x^3y^4=4x^3y^2(x^2+2xy+y^2)\)
\(=4x^3y^2(x+y)^2\)
9.
\(4x^5y^2+16x^4y^2-6x^3y^2=2x^3y^2(2x^2+4x-3)\)
13.
\(-3x^4y+6x^3y-3x^2y=-3x^2y(x^2-2x+1)=-3x^2y(x-1)^2\)
17.
\(8x^3-8x^2y+2xy^2=2x(4x^2-4xy+y^2)\)
\(=2x[(2x)^2-2.2x.y+y^2]=2x(2x-y)^2\)
21.
\((a^2+4)^2-16a^2b^2=(a^2+4)^2-(4ab)^2\)
\(=(a^2+4-4ab)(a^2+4+4ab)\)
25.
\(100a^2-(a^2+25)^2=(10a)^2-(a^2+25)^2\)
\(=(10a-a^2-25)(10a+a^2+25)\)
\(=-(a^2-10a+25)(a^2+10a+25)=-(a-5)^2(a+5)^2\)
29.
\(25a^2b^2-4x^2+4x-1=25a^2b^2-(4x^2-4x+1)\)
\(=(5ab)^2-(2x-1)^2=(5ab-2x+1)(5ab+2x-1)\)
a) \(2a^2x-5by-5a^2y+2by\)
\(=3\left(\frac{2}{3}a^2x-\frac{5}{3}a^2y\right)-3by\)
\(=3\left(\frac{2}{3}a^2x-\frac{5}{3}a^2y-by\right)\)