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1. C. \(16x^2\left(x-y\right)\)\(-10y\left(y-1\right)\)\(=-2\left(y-x\right)\)\(\left(8x^2+5y\right)\)
2. C. \(\left(x-y\right)\left(x-y-3\right)\)
3. D. \(\left(x-2\right)\left(x+1\right)\)
4. C. \(y\left(x-2\right)\)\(5x\left(x-3\right)\)
5. D. \(3\left(x-2y\right)\)
1. Trong các kết quả sau kết quả nào sai
A. -17x^3y-34x^2y^2+51xy^3=17xy(x^2+2xy-3y^2)
B. x(y-1) +3(y-1)= -(1-y)(x+3)
C. 16x^2(x-y)-10y(y-1)=-2(y-x)(8x^2+5y)
2. Đa thức (x-y)^2+3(y-x) được phân tích thành nhân tử là:
A. (x+y)(x-y+3)
B. (x-y)(2x-2y+3)
C. (x-y)(x-y-3)
D. Cả 3 câu đều sai
3. Kết quả phân tích đa thức x(x-2)+(x-2) thành nhân tử
A. (x-2)x
B. (x-2)^2.x
C. x(2x-4)
D. (x-2)(x+1)
4. Kết quả phân tích 5x^2(xy-2y)-15x(xy-2y) thành nhân tử
A. (xy-2y)(5x^2-15x^2)
B. y(x-2)(5x^2-15x^2)
C. y(x-2)5x(x-3)
D. (xy-2y)5x(x-3)
5. Kết quả phân tích đa thức 3x-6y thành nhân tử là
A. 3(x-6y)
B. 3(3x-y)
C. 3(3x-2y)
D. 3(x-2y)
a) x2-x-y2-y=(x2-y2)-(x+y)=(x+y)(x-y)-(x+y)=(x+y)(x-y-1)
b)x2-2xy+y2-z2=(x-y)2-z2=(x-y-z)(x-y+z)
c)5x-5y+ax-ay=5(x-y)+a(x-y)=(x-y)(5+a)
d)a3-a2x-ay+xy=a2(a-x)-y(a-x)=(a-x)(a2-y)
e)4x2-y2+4x+1=[(2x)2+2.2x.1+12]-y2=(2x+1)2-y2=(2x+1-y)(2x+1+y)
Chúc bạn học tốt!
a) 5x - 5y + ax - ay = 5(x - y) + a(x - y)
= (5 + a)(x - y)
b) x3 - x + 3x2y + 3xy2 + y3 - y
= (x3 + 3x2y + 3xy2 + y3) - (x + y)
= (x + y)3 - (x + y)
= (x + y)[(x + y)2 - 1]
= (x + y)(x + y + 1)(x + y - 1)
c) x2 - 2x - 3 = x2 + x - 3x -3
= x(x + 1) - 3(x + 1)
= (x - 3)(x + 1)
e) 6x - 9 - x2 = 3x - 9 + 3x - x2
= 3(x - 3) + x(3 - x)
= 3(x - 3) - x(x - 3)
= (3 - x)(x - 3)
bn post nhiều nên mình ghi đáp án thôi nhé phần nào sai đề mình cho qua
b)\(\left(x+1\right)\left(xy+1\right)\)
c)\(\left(a+b\right)\left(x+y\right)\)
d)\(\left(x-a\right)\left(x-b\right)\)
e)\(\left(x+y\right)\left(xy-1\right)\)
f)\(\left(a-b\right)\left(x^2+y\right)\)
\(5x-5y+ax-ay=5\left(x-y\right)+a\left(x-y\right)=\left(5+a\right)\left(x-y\right)\)
\(a^3-a^2x-ay+xy=a^2\left(a-x\right)-y\left(a-x\right)=\left(a^2-y\right)\left(a-x\right)\)
\(10x^2+10xy+5x+5y=10x\left(x+y\right)+5\left(x+y\right)=5\left(2x+1\right)\left(x+y\right)\) \(5ay-3bx+ax-15by=a\left(5y+x\right)-3b\left(5y+x\right)=\left(a-3b\right)\left(5y+x\right)\) \(x^3+x^2-x-1=x^2\left(x+1\right)-\left(x+1\right)=\left(x^2-1\right)\left(x+1\right)=\left(x+1\right)^2\left(x-1\right)\) \(2bx-3ay-6by+ax=x\left(2b+a\right)-3y\left(2b+a\right)=\left(x-3y\right)\left(2b+a\right)\)
\(x+2a\left(x-y\right)-y=\left(x-y\right)+2a\left(x-y\right)=\left(1+2a\right)\left(x-y\right)\)
1) x2 - x - y2 - y = (x - y)(x + y) - (x + y) = (x - y - 1)(x + y)
2. x2 - 2xy + y2 - z2 = (x - y)2 - z2 = (x - y - z)(x - y + z)
3. 5x - 5y + ax - ay = 5(x - y) + a(x - y) = (a + 5)(x - y)
4. a3 - a2x - ay + xy = a2(a - x) - y(a - x) = (a2 - y)(a - x)
5. 4x2 - y2 + 4x + 1 = (2x + 1)2 - y2 = (2x + 1 - y)(2x + y + 1)
6. x3 - x + y3 - y = (x + y)(x2 - xy + y2) - (x + y) = (x + y)(x2 - xy + y2 - 1)
Trả lời:
1, x2 - x - y2 - y
= ( x2 - y2 ) - ( x + y )
= ( x - y ) ( x + y ) - ( x + y )
= ( x + y ) ( x - y - 1 )
2, x2 - 2xy + y2 - z2
= ( x2 - 2xy + y2 ) - z2
= ( x - y )2 - x2
= ( x - y - z ) ( x - y + z )
3, 5x - 5y + ax - ay
= ( 5x + ax ) - ( 5y + ay )
= x ( 5 + a ) - y ( 5 + a )
= ( 5 + a ) ( x - y )
= ( 5 + a ) ( x - y )
4, a3 - a2x - ay + xy
= ( a3 - a2x ) - ( ay - xy )
= a2 ( a - x ) - y ( a - x )
= ( a - x ) ( a2 - y )
5, 4x2 - y2 + 4x + 1
= ( 4x2 + 4x + 1 ) - y2
= ( 2x + 1 )2 - y2
= ( 2x + 1 - y ) ( 2x + 1 + y )
6, x3 - x + y3 - y
= ( x3 + y3 ) - ( x + y )
= ( x + y ) ( x2 - xy + y ) - ( x + y )
= ( x + y ) ( x2 - xy + y - 1 )
\(a,3x^2+2x=x\left(3x+2\right)\)
\(b,5x-5y+ax-ay=5\left(x-y\right)+a\left(x-y\right)=\left(x-y\right)\left(5+a\right)\)
\(c,4x^2-25=\left(2x-5\right)\left(2x+5\right)\)
\(d,x^2+6x+5=x^2+x+5x+5=x\left(x+1\right)+5\left(x+1\right)=\left(x+1\right)\left(x+5\right)\)
\(e,x^2-y^2+2y-1=x^2-\left(y^2-2y+1\right)=x^2-\left(y-1\right)^2=\left(x-y+1\right)\left(x+y-1\right)\)
a ) 3x2 + 2x
= x. ( 3x + 2 )
b ) 5x - 5y + ax - ay
= ( 5x + ax ) - ( 5y + ay )
= x.( 5 + a ) - y ( 5 + a )
= ( 5 + a ) ( x - y )
c ) 4x2 - 25
= ( 2x + 5 ) ( 2x - 5 )
d ) x2 + 6x + 5
= x2 + x + 5x + 5
= x.( x + 1 ) + 5.( x + 1 )
= ( x + 1 ) ( x + 5 )
e ) x2 - y2 + 2y - 1
= x2 - ( y - 1 )2
= ( x - y + 1 ) ( x + y - 1 )
f ) x3 - 3x + 2
= x3 + 2x2 - 2x2 - 4x + x + 2
= x2 ( x + 2 ) - 2x ( x + 2 ) + ( x + 2 )
= ( x + 2 ) ( x2 - 2x + 1 )
= ( x + 2 ) ( x - 1 )2
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