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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 )
Lời giải:
31.
\(2a^2x-5by-6a^2y+2bx=(2a^2x+2bx)-(5by+5a^2y)\)
\(=2x(a^2+b)-5y(b+a^2)=(a^2+b)(2x-5y)\)
34.
\(4acx+4bcx+4ax+4bx=4x(ac+bc+a+b)\)
\(=4x[(ac+bc)+(a+b)]=4x[c(a+b)+(a+b)]=4x(c+1)(a+b)\)
37. Sửa đề:
\(2ax^2-bx^2-2ax+bx+4a-2b\)
\(=(2ax^2-bx^2)-(2ax-bx)+(4a-2b)\)
\(=x^2(2a-b)-x(2a-b)+2(2a-b)=(2a-b)(x^2-x+2)\)
Câu 31:
\(2a^2x-5by-5a^2y+2bx\)
\(=2x\left(a^2+b\right)-5y\left(a^2+b\right)\)
\(=\left(a^2+b\right)\left(2x-5y\right)\)
Câu 34:
\(4acx+4bcx+4ax+4bx\)
\(=4cx\left(a+b\right)+4x\left(a+b\right)\)
\(=\left(a+b\right)\left(4cx+4x\right)\)
\(=4x\left(a+b\right)\left(c+1\right)\)
Câu 37:
\(2ax^2-bx^2-2ax+bx+4a-2b\)
\(=x^2\left(2a-b\right)-x\left(2a-b\right)+2\left(2x-b\right)\)
\(=\left(2a-b\right)\left(x^2-x+2\right)\)
\(=\left(2a-b\right)\left(x^2-x+2\right)\)
\(1,2x^2-6xy+5x-15y\)
\(=2x\left(x-3y\right)+5\left(x-3y\right)\)
\(=\left(x-3y\right)\left(2x+5\right)\)
\(2,ax^{2\:}-3axy+bx-3by\)
\(=ax\left(x-3y\right)+b\left(x-3y\right)\)
\(=\left(x-3y\right)\left(ax+b\right)\)
\(3,5ax^2-3axy+3ay^2-3axy\) ( Đề sai )
Sửa : \(3ax^2-3axy+3ay^2-3axy\)
\(=3ax\left(x-y\right)+3ay\left(y-x\right)\)
\(=3ax\left(x-y\right)-3ay\left(x-y\right)\)
\(=3a\left(x-y\right)^2\)
\(4,4acx+4bcx+4ax+4bx\)
\(=4cx\left(a+b\right)+4x\left(a+b\right)\)
\(=4x\left(a+b\right)\left(c+1\right)\)
\(6,ax^{2\:}y-bx^2y-ax+bx+2a-2b\)
\(=x^2y\left(a-b\right)-x\left(a-b\right)+2\left(a-b\right)\)
\(=\left(a-b\right)\left(x^2y-x+2\right)\)
\(7,ax^{2\:}-bx^2-2ax+2bx-3a+3b\)
\(=x^2\left(a-b\right)-2x\left(a-b\right)-3\left(a-b\right)\)
\(=\left(a-b\right)\left(x^2-2x-3\right)\)
\(8,ax^{2\:}-5x^2-ax+5x+a-5\)
\(=x^2\left(a-5\right)-x\left(a-5\right)+\left(a-5\right)\)
\(=\left(a-5\right)\left(x^2-x+1\right)\)
\(9,ax+bx+cx-2a-2b+2c\) Đề sai
Sửa :\(ax+bx+cx-2a-2b-2c\)
\(=x\left(a+b+c\right)-2\left(a+b+c\right)\)
\(=\left(a+b+c\right)\left(x-2\right)\)
\(10,2ax-bx+3cx-2a+b-3c\)
\(=\left(2ax-2a\right)-\left(bx-b\right)+\left(3cx-3c\right)\)
\(=2a\left(x-1\right)-b\left(x-1\right)+3c\left(x-1\right)\)
\(=\left(x-1\right)\left(2a-b+3c\right)\)
Mấy câu đề sai mk sửa chỗ nào ko đúng thì nói mk nha !
a) \(2a^2x-5by-5a^2y+2by\)
\(=3\left(\frac{2}{3}a^2x-\frac{5}{3}a^2y\right)-3by\)
\(=3\left(\frac{2}{3}a^2x-\frac{5}{3}a^2y-by\right)\)
Đặt : \(A=ax^2+a-2ax+b-2bx+bx^2\)
\(=\left(ax^2+a-2ax\right)+\left(b-2bx+bx^2\right)\)
\(=a\left(x^2+1-2x\right)+b\left(1-2x+x^2\right)\)
\(=a\left(x^2-2x+1\right)+b\left(x^2-2x+1\right)\)
\(=a\left(x-1\right)^2+b\left(x-1\right)^2\)
\(=\left(x-1\right)^2\left(a+b\right)\)
a) \(x^3-2x^2+2x-1^3\)
\(=x\left(x^2-2x+1\right)+x-1\)
\(=x\left(x-1\right)+\left(x-1\right)\)
\(=\left(x+1\right)\left(x-1\right)\)
b) \(x^2y+xy+x+1\)
\(=xy\left(x+1\right)+\left(x+1\right)\)
\(=\left(xy+1\right)\left(x+1\right)\)
c) \(ax+by+ay+bx\)
\(=a\left(x+y\right)+b\left(x+y\right)\)
\(=\left(a+b\right)\left(x+y\right)\)
d) \(x^2-\left(a+b\right)x+ab\)
\(=x^2-ax-bx+ab\)
\(=\left(x^2-ax\right)-\left(bx-ab\right)\)
\(=x\left(x-a\right)-b\left(x-a\right)\)
\(=\left(x-b\right)\left(x-a\right)\)
e) Ko biết làm
f) \(ax^2+ay-bx^2-by\)
\(=\left(ax^2+ay\right)-\left(bx^2+by\right)\)
\(=a\left(x^2+y\right)-b\left(x^2+y\right)\)
\(=\left(a-b\right)\left(x^2+y\right)\)
\(2ax^2-bx^2-2ax+bx+4a-2b\)
\(=\left(2ax^2-2ax+4a\right)-\left(bx^2-bx+2b\right)\)
\(=2a\left(x^2-x+2\right)-b\left(x^2-x+2\right)\)
\(=\left(2a-b\right)\left(x^2-x+2\right)\)
Tiếp đi~~
2ax2 - bx2 - 2ax + bx + 4a - 2b
= (2ax2 - 2ax + 4a) - (bx2 - bx + 2b)
= 2a.(x2 - x + 2) - b.(x2 - x + 2)
= (x2 - x + 2).(2a - b)
= (x2 - 2x + x + 2).(2a - b)
= [-x.(x + 2) + (x + 2)].(2a - b)
= (x + 2).(1 - x).(2a - b)