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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 )
A = 10ax - 5ay - 2x + y
= ( 10ax - 5ay ) - ( 2x - y )
= 5a( 2x - y ) - ( 2x - y )
= ( 2x - y )( 5a - 1 )
B = 2x2 - 6xy + 5x - 15y
= 2x( x - 3y ) + 5( x - 3y )
= ( x - 3y )( 2x + 5 )
C = ax2 - 3axy + bx - 3by
= ( ax2 + bx ) - ( 3axy + 3by )
= x( ax + b ) - 3y( ax + b )
= ( ax + b )( x - 3y )
D = 2ax3 + 6ax2 + 6ax + 18a
= 2ax2( x + 3 ) + 6a( x + 3 )
= ( x + 3 )( 2ax2 + 6a )
= ( x + 3 )2a( x2 + 3 )
E = 5x2y + 5xy2 + a2x + a2y ( đã sửa 1 dấu '-' )
= 5xy( x + y ) + a2( x + y )
= ( x + y )( 5xy + a2 )
F = 10xy2 - 5by2 + 2a2x - aby ( xem lại đề chứ không phân tích được :)) )
1 ) \(x\left(a-b\right)+a-b=\left(x+1\right)\left(a-b\right)\)
2 ) \(2x\left(b-a\right)+a-b=2x\left(b-a\right)-\left(b-a\right)=\left(2x-1\right)\left(b-a\right)\)
3 ) \(-2x-2y+ax+ay=-2\left(x+y\right)+a\left(x+y\right)=\left(a-2\right)\left(x+y\right)\)
4 ) \(x^2-xy-2x+2y=x\left(x-y\right)-2\left(x-y\right)=\left(x-2\right)\left(x-y\right)\)
5 ) \(5x^2y+5xy^2+a^2x+a^2y\)
\(=5xy\left(x+y\right)+a^2\left(x+y\right)\)
\(=\left(5xy+a^2\right)\left(x+y\right)\)
6 ) \(2x^2-6xy+5x-15y\)
\(=2x\left(x-3y\right)+5\left(x-3y\right)\)
\(=\left(2x+5\right)\left(x-3y\right)\)
7 ) \(ax^2-3axy+bx-3by\)
\(=\left(ax^2+bx\right)-\left(3axy+3by\right)\)
\(=x\left(ax+b\right)-3y\left(ax+b\right)\)
\(=\left(x-3y\right)\left(ax+b\right)\)
8 ) \(x^2+4x-5x-20=0\)
\(\Leftrightarrow x\left(x+4\right)-5\left(x+4\right)=0\)
\(\Leftrightarrow\left(x-5\right)\left(x+4\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x-5=0\\x+4=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=5\\x=-4\end{matrix}\right.\)
9 ) \(x^2+10x-2x-20=0\)
\(\Leftrightarrow x\left(x+10\right)-2\left(x+10\right)=0\)
\(\Leftrightarrow\left(x-2\right)\left(x+10\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x-2=0\\x+10=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=2\\x=-10\end{matrix}\right.\)
10 ) \(x^2-6x-4x+24=0\)
\(\Leftrightarrow x\left(x-6\right)-4\left(x-6\right)=0\)
\(\Leftrightarrow\left(x-4\right)\left(x-6\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x-4=0\\x-6=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=4\\x=6\end{matrix}\right.\)
:D
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:
\(2ax^2-bx^2-2ax+bx+4a-2b\)
\(=x^2\left(2a-b\right)-x\left(2a-b\right)+2\left(2x-b\right)\)
\(=\left(2a-b\right)\left(x^2-x+2\right)\)
\(=\left(2a-b\right)\left(x^2-x+2\right)\)
Bài 2: Phân tích các đa thức sau thành nhân tử ( phương pháp nhóm hạng tử ) .
a) ax2 - 5x2 - ax + 5x + a - 5;
= ( ax2 - 5x2) - (ax - 5x) + (a - 5)
= x2(a - 5) - x(a - 5) + (a - 5)
= (a - 5) (x2 - x + 1)
b) ax - bx + cx - 3a + 3b - 3c
= ( ax - bx + cx) - (3a - 3b + 3c)
= x(a - b + c) - 3(a - b + c)
= (a - b + c)(x - 3)
1. = 2(a+b)
2. =2(a-b)
3.=2(a+2b-3c)
4.=3(a-2b-3c)
5.=-4(a+2b+3c)
6.=-5(x+2xy+3y)
7.=-7(a+2ab+3b)
8.=6(xy-2x-3y)
9.=8(xy-3y+2x)
10.=9(ab-2a+1)
Lần sau bn cần ghi đề rõ ràng hơn 
11.=x(y-1)
12.=a(x+1)
13.=m(x+y+1)
14.=-a(x+y+1)
15.=-a(x2+x+1)
16.=-2a(x+2y)
17.=2a(x-y+1)
18.=2(2ax-ay-2)
19.=5a(1-2x-3)
20.=-2ab(a+2b+3)
d) \(ax^2-5x^2-ax+5x+a-5=\left(ax^2-ax+a\right)+\left(-5x^2+5x-5\right)\)
\(=a\left(x^2-x+1\right)-5\left(x^2-x+1\right)=\left(a-5\right)\left(x^2-x+1\right)\)
e) \(ax-bx-2cx-2a+2b+4c=x\left(a-b-2c\right)-2\left(a-b-2c\right)\)
\(=\left(x-2\right)\left(a-b-2c\right)\)
1) x - y - a(x - y) = (x - y) - a(x - y) = (1 - x)(x - y)
2) a - b + x(a - b) = (a - b) + x(a - b) = (1 + x)(a - b)
3) a(x - y) - x + y = a(x - y) - (x - y) = (a - 1)(x - y)
4) x(a - b) - a + b = x(a - b) - (a - b) = (x - 1)(a - b)
5) ax + ay + bx + by = a(x + y) + b(x + y) = (a + b)(x + y)
6) ax + ay - bx - by = a(x + y) - b(x + y) = (a - b)(x + y)
7) - 2x - 2y + ax + ay = -2(x + y) + a(x + y) = (a - 2)(x + y)
8) x2 - xy - 2x + 2y = x(x - y) - 2(x - y) = (x - 2)(x - y)
Sorry nha, giờ mình chỉ rảnh làm 8 câu thôi
1, 2a+2b = 2( a + b )
2, 2a-2b = 2( a - b )
3, 2a+4b-6c = 2( a + 2b - 3c )
4, 3a-6b-9c = 3( a - 2b - 3c )
5, xy-x = x( y - 1 )
6, -5x-10xy-15y = -5( x + 2xy + 3y )
7, -7a-14ab-21b = -7( a + 2ab + 3b )
8, 6xy-12x-18y = 6 ( xy - 2x - 3y )
9, 8xy-24y+16x = 8 ( xy - 3y + 2x )
10, 9ab-18a+9 = 9( ab - 2a + 1 )
11, ax+a = a( x + 1 )
12, mx+my+m = m( x + y + 1 )
13, -ax-ay-a = -a( x + y +1 )
14, -2ax-4ay = -2a( x + 2y )
15, 2ax-2ay+2a = 2a( x - y + 1 )
16, 4ax-2ay-2 = 2( 2ax - a - 1 )
17, 5a-10ax-15a = 5a( 1 - 2x - 3 ) = 5a( -2x - 2 )
18, 5ax-15ay+20a = 5a( x - 3y + 4 )
19, 3a2x-6a2y+12a = 3a( ax - 2ay + 4 )
20, 2axy-4a2xy2+6a3x\(^2\) = 2ax( y - 2ay\(^2\) + 3a\(^2\)x )
\(1,2x^2-6xy+5x-15y\)
\(=2x\left(x-3y\right)+5\left(x-3y\right)\)
\(=\left(x-3y\right)\left(2x+5\right)\)
\(2,ax^{2\:}-3axy+bx-3by\)
\(=ax\left(x-3y\right)+b\left(x-3y\right)\)
\(=\left(x-3y\right)\left(ax+b\right)\)
\(3,5ax^2-3axy+3ay^2-3axy\) ( 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 !