Phân tích đa thức thành nhân tử :
1) x( a-b) + a - b
2) x ( a+ b ) - a - b
3 ) 10 ax - 5ay - 2x + y
4 ) \(2a^2x-5by-5a^2y+2bx\)
5 ) \(2ax^2-bx^2-2ax+bx+4a-2b\)
Giups mình vs . mai p nộp r TT
Phân tích đa thức sau bằng phương pháp nhóm hạng tử
1) x ( a - b ) + a - b ; 2) x - y - a( x - y ) ; 3) a( x + y ) - x - y ; 4) x( a - b ) - a + b ; 5) x\(^2\) + xy - 2x - 2y
6) 10ax - 5ay + 2x - y ; 7) 2a\(^{^2}\) x - 5by - 5a\(^2\) y + 2bx ; 8) 2ax\(^2\)- bx\(^2\) - 2ax + bx + 4a - 2b ; 9) 2ax - bx + 3cx - 2a + b - 3c
10) ax - bx - 2cx - 2a + 2b + 4c
1, x(a-b)+a-b 2, x-y-a(x-y) 3, a(x+y)-x-y 4, x(a-b)-a+b 5, x2+xy-2x-2y 6, 10ax-5ay+2x-y
= x(a-b)+(a-b) =(x-y)-a(x-y) =a(x+y)-(x+y) =x(a-b)-(a-b) =(x2+xy)-(2x+2y) =(10ax+2x)-(5ay+y)
=(a-b)(x+1) =(x-y)(1-a) =(x+y)(a-1) =(a-b)(x-1) =x(x+y)-2(x+y) =2x(5a+1)-y(5a+1)
=(x+y)(x-2) =(5a+1)(2x-y)
7, 2a2x-5by-5a2y+2bx 8, 2ax2-bx2-2ax+bx+4a-2b 9, 2ax-bx+3cx-2a+b-3c 10, ax-bx-2cx-2a+2b+4c
=(2a2x+2bx)-(5by+5a2y) =(2ax2-bx2)-(2ax-bx)+(4a-2b) =(2ax-2a)-(bx-b)+(3cx-3c) =(ax-2a)-(bx-2b)-(2cx-4c)
=2x(a2+b)-5y(b+a2) =x2(2a-b)-x(2a-b)+2(2a-b) =2a(x-1)-b(x-1)+3c(x-1) =a(x-2)-b(x-2)-2c(x-2)
=(a2+b)(2x-5y) =(2a-b)(x2-x+2) =(x-1)(2a-b+3c) =(x-2)(a-b-2c)
1, 6a^2y-3aby+4a^2x-2abx
2, 5x^2y-5xy^2-a^2x+a^2y
3, 2x^2-6xy+5x-15y
4, ax^2-5by-5a^2y+2bx
5, 2ax^3+6ax^2+6ax+18a
6, ax^2-bx^2y-ã+bx+2a-2b
7,3ax^2+3bx^2+ã+bx+5a=5b
8, ax^2-bx^2-2ax+2bx-3a+3b
9, 2ax^2-bx^2-2ax+bx-3a+3b
10, 2ax^2-5x^2-ax+bx+4a-2b
11,ax^2-5x^2-ax+5x+a-5
Phân tích đa thức thành nhân tử:
a)A=4acx+4bcx+4x+4bx
b)B=ax-bx+cx-3a+3b-3c
c)C=2ax-bx+3cx-2a+b-3c
d)D=ax-bx-2cx-2a+2b+4c
e)E=3ax2+3bx2+ax+bx+5a+5b
f)F=ax2-bx2-2ax+2bx-3a+3b
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 )
Phân tích thành nhân tử (mọi người làm chi tiết ạ)
\(2ax-bx+3cx-2a+b-3c\)
\(ax-bx-2cx-2a+2b+4c\)
\(3ax^2 +3bx^2 +ax+bx+5a+5b\)
\(ax^2 -bx^2 -2ax+2bx-3a+3b\)
\(2ax-bx+3cx-2a+b-3c\\ =x\left(2a-b+3c\right)-\left(2a-b+3c\right)\\ =\left(x-1\right)\left(2a-b+3c\right)\)
\(ax-bx-2cx-2a+2b+4c\\ =x\left(a-b-2c\right)-2\left(a-b-2c\right)\\ =\left(x-2\right)\left(a-b-2c\right)\)
\(3ax^2+3bx^2+ax+bx+5a+5b\\ =3x^2\left(a+b\right)+x\left(a+b\right)+5\left(a+b\right)\\ =\left(3x^2+x+5\right)\left(a+b\right)\)
\(ax^2-bx^2-2ax+2bx-3a+3b\\ =x^2\left(a-b\right)-2x\left(a-b\right)-3\left(a+b\right)\\ =\left(x^2-2x-3\right)\left(a+b\right)\\ =\left(x+1\right)\left(x-3\right)\left(a+b\right)\)
phân tích
2a^2x-5by-5a^2y+2by
2ax^2-bx^2-2ax+bx+4a-2b
5x^2+10xy+5y^2
25a^2b^2-4x^2+4x-1
a) \(2a^2x-5by-5a^2y+2by\)
\(=3\left(\frac{2}{3}a^2x-\frac{5}{3}a^2y\right)-3by\)
\(=3\left(\frac{2}{3}a^2x-\frac{5}{3}a^2y-by\right)\)
Giúp vs ạ c.ơn rất nhiều !
Phân tích đa thức thành nhân tử
a, a^2 + b^2 + 2ab + 2a + 2b + 1
b, ax^2 - bx^2 - 2bc + 2ax + a
a) \(a^2+b^2+2ab+2a+2b+1=\left(a^2+2ab+b^2\right)+\left(2a+2b\right)+1\)
\(=\left(a+b\right)^2+2\left(a+b\right)+1=\left[\left(a+b\right)+1\right]^2=\left(a+b+1\right)^2\)
b) K phân tích dc.
Phân tích đa thức thành nhân tử
x^2-xy+2x-2y
ax+ay-2x-2y
ax^2-3axy+bx-3by
2a^2-5by-5a^2y+2bx
x2-xy+2x-2y
= (x2-xy)+(2x-2y)
= x(x-y)+2(x-y)
= (x-y)(x+2)
ax+ay-2x-2y
= (ax+ay)-(2x+2y)
= a(x+y)-2(x+y)
=(x+y)(a-2)
ax2-3axy+bx-3by
= (ax2+bx)-(3axy+3by)
= x(ax+b)-3y(ax+b)
= (ax+b)(x-3y)
2a2-5by-5a2y+2bx
= (2a2-5a2y)+(2bx-5by)
= a2(2-5y)+b(2x-5y)
x2-xy+2x-2y=(x2-xy)+(2x-2y)=x(x-y)+2(x-y)=(x-y)(x+2)
ax+ay-2x-2y=(ax+ay)-(2x+2y)=a(x+y)-2(x+y)=(x+y)(a-2)
ax2-3axy+bx-3by=(ax2+bx)-(3axy+3by)=x(ax+b)-3y(ax+b)=(ax+b)(x-3y)
Phân tích thành nhân tử :
1, \(2ax^2-bx^2-2ax+bx+4a-2b\)
2, \(ax^2y-bx^2y-ax+bx+2a-2b\)
3, \(49\cdot\left(x-y\right)^2-25\cdot\left(y-1\right)^2\)
Phân tích thành nhân tử (mọi người làm chi tiết ạ)
\(ax^2 -3axy+bx-3by\)
\(5x^2 y+5xy^2 -a^2 x-a^2 y\)
\(2ax^3 +6ax^2 +6ax+18a\)
\(10xy^2 -5by^2 +2ax-ab\)
\(ax-bx+cx-3a+3b-3c\)
\(ax^2-3axy+bx-3by\\ =x\left(ax+b\right)-3y\left(ax+b\right)\\ =\left(x-3y\right)\left(ax+b\right)\)
\(5x^2y+5xy^2-a^2x-a^2y\\ =5xy\left(x+y\right)-a^2\left(x+y\right)\\ =\left(5xy-a^2\right)\left(x+y\right)\)
\(2ax^3+6ax^2+6ax+18a\\ =2ax^2\left(x+3\right)+6a\left(x+3\right)\\ =2a\left(x^2+3\right)\left(x+3\right)\)
\(10xy^2-5by^2+2ax-ab\\ =5y^2\left(2x-b\right)+a\left(2x-b\right)\\ =\left(5y^2+a\right)\left(2x-b\right)\)
\(ax-bx+cx-3a+3b-3c\\ =x\left(a-b+c\right)-3\left(a-b+c\right)\\ =\left(x-3\right)\left(a-b+c\right)\)