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bài 1: a) \(x^2-3=x^2-\left(\sqrt{3}\right)^2=\left(x+\sqrt{3}\right)\left(x-\sqrt{3}\right)\)
b) \(\left(a+b\right)^2-\left(a+b\right)^2=\left(a+b+a+b\right)\left(a+b-a-b\right)=2a+2b=2\left(a+b\right)\)
c) \(x^3-27b^3=\left(x-3b\right)\left(x^2+3xb+b^2\right)\)
\(x^4+5x^3-12x^2+5x+1\)
\(=x^4-x^3+6x^3-6x^2-6x^2+6x-x+1\)
\(=x^3\left(x-1\right)+6x^2\left(x-1\right)-6x\left(x-1\right)-\left(x-1\right)\)
\(=\left(x-1\right)\left(x^3+6x^2-6x-1\right)\)
\(=\left(x-1\right)\left(x^3-x^2+7x^2-7x+x-1\right)\)
\(=\left(x-1\right)\left[x^2\left(x-1\right)+7x\left(x-1\right)+\left(x-1\right)\right]\)
\(=\left(x-1\right)\left(x^2+7x+1\right)\)
A = 6x4 - 5x3 + 4x2 + 2x - 1
= 6x4 + 3x3 - 8x3 - 4x2 + 8x2 + 4x - 2x - 1
= 3x3. ( 2x + 1 ) - 4x2 ( 2x + 1 ) + 4x ( 2x + 1 ) - ( 2x + 1 )
= ( 2x + 1 ) ( 3x3 - 4x2 + 4x - 1 )
= ( 2x + 1 ) ( 3x3 - x2 - 3x2 + x + 3x - 1 )
= ( 2x + 1 ) [ x2 ( 3x - 1 ) - x ( 3x - 1 ) + ( 3x - 1 ) ]
= ( 2x + 1 ) ( 3x - 1 ) ( x2 - x + 1 )
B = 4x4 + 4x3 + 5x2 + 8x - 6
= 4x4 - 2x3 + 6x3 - 3x2 + 8x2 - 4x + 12x - 6
= 2x3 ( 2x - 1 ) + 3x2 ( 2x - 1 ) + 4x ( 2x - 1 ) + 6 ( 2x - 1 )
= ( 2x - 1 ) ( 2x3 + 3x2 + 4x + 6 )
= ( 2x - 1 ) [ x2 ( 2x + 3 ) + 2 ( 2x + 3 ) ]
= ( 2x - 1 ) ( 2x + 3 ) ( x2 + 2 )
C = x4 + x3 - 5x2 + x - 6
= x4 - 2x3 + 3x3 - 6x2 + x2 - 2x + 3x - 6
= x3 ( x - 2 ) + 3x2 ( x - 2 ) + x ( x - 2 ) + 3 ( x - 2 )
= ( x - 2 ) ( x3 + 3x2 + x + 3 )
= ( x - 2 ) [ x2 ( x + 3 ) + ( x + 3 ) ]
= ( x - 2 ) ( x + 3 ) ( x2 + 1 )
a)x^2-(a+b)x+ab
= x^2 - ax - bx + ab
= (x^2 - ax) - (bx - ab)
= x(x-a) - b(x-a)
= (x-b)(x-a)
b)7x^3-3xyz-21x^2+9z
=
c)4x+4y-x^2(x+y)
= 4(x + y) - x^2(x+y)
= (4-x^2) (x+y)
= (2-x)(2+x)(x+y)
d) y^2+y-x^2+x
= (y^2 - x^2) + (x+y)
= (y-x)(y+x)+ (x+y)
= (y-x+1) (x+y)
e)4x^2-2x-y^2-y
= [(2x)^2 - y^2] - (2x +y)
= (2x-y)(2x+y) - (2x+y)
= (2x -y -1)(2x+y)
f)9x^2-25y^2-6x+10y
=
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)
d, \(x^8+x^7+1\)
\(=x^8-x^2+x^7-x+x^2+x+1\)
\(=x^2\left(x^6-1\right)+x\left(x^6-1\right)+x^2+x+1\)
\(=x^2\left(x^3-1\right)\left(x^3+1\right)+x\left(x^3-1\right)\left(x^3+1\right)+x^2+x+1\)
\(=\left(x^5+x^2\right)\left(x^3-1\right)+\left(x^4+x\right)\left(x^3-1\right)+x^2+x+1\)
\(=\left(x^3-1\right)\left(x^5+x^4+x^2+x\right)+x^2+x+1\)
\(=\left(x^2+x+1\right)\left(x-1\right)\left(x^5+x^4+x^2+x\right)+x^2+x+1\)
\(=\left(x^2+x+1\right)\left(x^6-x^4+x^3-x\right)+x^2+x+1\)
\(=\left(x^2+x+1\right)\left(x^6-x^4+x^3-x+1\right)\)
c, \(x^4+5x^3-12x^2+5x+1\)
\(=x^4-x^3+6x^3-6x^2-6x^2+6x-x+1\)
\(=x^3\left(x-1\right)+6x^2\left(x-1\right)-6x\left(x-1\right)-\left(x-1\right)\)
\(=\left(x-1\right)\left[x^3+6x^2-6x-1\right]\)
\(=\left(x-1\right)\left[\left(x-1\right)\left(x^2+x+1\right)+6x\left(x-1\right)\right]\)
\(=\left(x-1\right)\left(x-1\right)\left(x^2+7x+1\right)\)
\(=\left(x-1\right)^2.\left(x^2+7x+1\right)\)
a, \(\left(x^2+x-2\right)\left(x^2+9x+18\right)-28\)
\(=\left(x-1\right)\left(x+2\right)\left(x+3\right)\left(x+6\right)-28\)
\(=\left[\left(x-1\right)\left(x+6\right)\right].\left[\left(x+2\right)\left(x+3\right)\right]-28\)
\(=\left(x^2+5x-6\right)\left(x^2+5x+6\right)-28\)
\(=\left(x^2+5x\right)^2-36-28\)
\(=\left(x^2+5x\right)^2-64\)
\(=\left(x^2+5x-8\right)\left(x^2+5x+8\right)\)
b, \(B=\left(x+1\right)^2\left(2x+3\right)-18\)
\(=\left(4x^2+8x+3\right)\left(x^2+2x+1\right)-18\)
Đặt \(x^2+2x+1=t\Rightarrow4x^2+8x+3=4t-1\)
Ta có: \(B=\left(4t-1\right)t-18\)
\(=4t^2-t-18\)
\(=4t^2-9t+8t-18\)
\(=t\left(4t-9\right)+2\left(4t-9\right)\)
\(=\left(4t-9\right)\left(t+2\right)\)
\(=\left(4x^2+8x-5\right)\left(x^2+2x+3\right)\) (vì \(t=x^2+2x+1\)
\(=\left(2x-1\right)\left(2x+5\right)\left(x^2+2x+3\right)\)
Chúc bạn học tốt.