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4a2=4b2-4a+1
=(2a)2-2*2a*1+12-4b2= (2a-1)2-(2b)2(2a-1-2b)(2a-1+2b)
a) \(3xy^2-12xy+12x\)
\(=3x\left(y-4y+4\right)\)
b) \(3x^3y-6x^2y-3xy^3-6axy^2-3a^2xy+3xy\)
\(=3xy\left(x^2-2x-y^2-2ay-a^2+1\right)\)
\(=3xy\left[\left(x^2-2\cdot x\cdot1+1^2\right)-\left(y^2+2\cdot y\cdot a+a^2\right)\right]\)
\(=3xy\left[\left(x-1\right)^2-\left(y+a\right)^2\right]\)
\(=3xy\left(x-1-y-a\right)\left(x-1+y+a\right)\)
c) \(36-4a^2+20ab-25b^2\)
\(=6^2-\left[\left(2a\right)^2-2\cdot2a\cdot5b+\left(5b\right)^2\right]\)
\(=6^2-\left(2a-5b\right)^2\)
\(=\left(6-2a+5b\right)\left(6+2a-5b\right)\)
d) \(5a^3-10a^2b+5ab^2-10a+10b\)
\(=5a\left(a^2-2ab+b^2\right)-10\left(a-b\right)\)
\(=5a\left(a-b\right)^2-10\left(a-b\right)\)
\(=\left(a-b\right)\left[5a\left(a-b\right)-10\right]\)
\(=5\left(a-b\right)\left[a\left(a-b\right)-2\right]\)
\(=5\left(a-b\right)\left(a^2-ab-2\right)\)
a. 3xy2-12xy+12x
= 3x(y2-4y+4)
= 3x(y-2)2
b. 3x3y-6x2y-3xy3-6axy2-3a2xy+3xy
= 3xy( x2-2x-y2-2ay-a2+1)
= 3xy ((x2-2x+1)-(a2-2ay-y2))
=3xy((x-1)2-(a-y)2)
= 3xy((x-1+a-y)(x-1-(a-y))
=3xy(x-1+a-y)(x-1-a+y)
d. =( 5a(a2-2ab+b2))-(10(a+b))
= 5a(a-b)2-10(a-b)
=5a(a-b)(a-b)-10(a-b)
=(a-b)(5a(a-b)-10)
Hình như mik làm sai hết rồi
Bài 1: 4a2-4ab+b2-9a2b2
=(2a)2-2.2a.b+b2-(3ab)2
=(2a-b)2-(3ab)2
=(2a-b-3ab)(2a-b+3ab)
a/ (4a2-4ab+b2)-9a2b2
= (2a-b)2-(3ab)2
= (2a-b-3ab) (2a-b+3ab)
b)\(2a^2-3+5a\)
\(=\left(2a^2+6a\right)-\left(a+3\right)\)
\(=\left(a+3\right)\left(2a-1\right)\)
d)\(2a^2-5-3a\)
\(=\left(2a^2+2a\right)-\left(5a+5\right)\)
\(=\left(a+1\right)\left(2a-5\right)\)
a) \(a^2-3-2a\)
\(=a^2-2a+1-4\)
\(=\left(a^2-2a+1\right)-2^2\)
\(=\left(a-1\right)^2-2^2\)
\(=\left(a-1-2\right)\left(a-1+2\right)\)
\(=\left(a-3\right)\left(a+1\right)\)
c) \(4a+a^2+3\)
\(=a^2+4a+4-1\)
\(=\left(a^2+4a+4\right)-1^2\)
\(=\left(a+2\right)^2-1^2\)
\(=\left(a+2-1\right)\left(a+2+1\right)\)
\(=\left(a+1\right)\left(a+3\right)\)
\(3y^2\left(a-3x\right)-a\left(a-3x\right)=\left(3y^2-a\right)\left(a-3x\right)\)
Phân tích đa thức thành nhân tử
a) (1-2x)(1+2x)-x(x+2)(x-2)
\(=1-4x^2-x\left(x^2-4\right)\)
\(=1-4x^2-x^3+4x\)
\(=\left(1-x^3\right)+\left(4x-4x^2\right)\)
\(=\left(1-x\right)\left(1+x+x^2\right)+4x\left(1-x\right)\)
\(=\left(1-x\right)\left(1+x+x^2+4x\right)\)
\(=\left(1-x\right)\left(x^2+5x+1\right)\)
\(a\left(a+2b\right)^3-b\left(2a+b\right)^3\)
\(=a\left(a^3+6a^2b+12ab^2+8b^3\right)-b\left(8a^3+12a^2b+6ab^2+b^3\right)\)
\(=a^4+6a^3b+12a^2b^2+8b^3a-8a^3b-12a^2b^2+6ab^3-b^4\)
\(=a^4+6a^3b+8b^3a-8a^3b-6ab^3-b^4\)
\(=\left(a^4-b^4\right)+\left(6a^3b-6ab^3\right)+\left(8b^3a-8a^3b\right)\)
\(=\left(a-b\right)\left(a^3+a^2b+ab^2+b^3\right)+6ab\left(a^2-b^2\right)+8ab\left(b^2-a^2\right)\)
\(=\left(a-b\right)\left(a^3+a^2b+ab^2+b^3\right)+6ab\left(a-b\right)\left(a+b\right)-8ab\left(a-b\right)\left(a+b\right)\)
\(=\left(a-b\right)\left(a^3+a^2b+ab^2+b^3+6a^2b+6ab^2-8a^2b-8ab^2\right)\)
\(=\left(a-b\right)\left(a^3-a^2b-ab^2+b^3\right)\)
\(=\left(a-b\right)\left[a^2\left(a-b\right)-b^2\left(a-b\right)\right]\)
\(=\left(a-b\right)^3\left(a+b\right)\)
a)27x3+27x2+9x+1+x+1/3
=(3x+1)3+1/3(3x+1)
=(3x+1)[(3x+1)2+1/3]
=(3x+1)(9x2+6x+4/3)
b)8xy3-5xyz-24y2+15z
=(8xy3-24y2)-(5xyz-15z)
=8y2(xy-3)-5z(xy-3)
=(xy-3)(8y2-5z)
c)x4+x3+x+1
=x3(x+1)+(x+1)
=(x+1)(x3+1)
=(x+1)(x+1)(x2-x+1)
=(x+1)2(x2-x+1)
d)a6-a4-2a3+2a2
=a4(a-1)(a+1)-2a2(a-1)
=(a-1)(a5+a4-2a2)
=(a-1)(a5-a4+2a4-2a2)
=(a-1)[a4(a-1)+2a2(a-1)(a+1)]
=(a-1)(a-1)(a4+2a3+2a2)
=(a-1)2(a4+2a3+2a2)
\(x^4+x^3+x+1\)
\(=x^3\left(x+1\right)+\left(x+1\right)\)
\(=\left(x+1\right)\left(x^3+1\right)\)
\(=\left(x+1\right)^2\left(x^2-x+1\right)\)
a) \(-5x^2+16x-3=-5x^2+15x+x-3=-5x\left(x-3\right)+x-3=\left(x-3\right)\left(1-5x\right).\)
b) \(x^4+64=x^4+16x^2+64-16x^2=\left(x^2+8\right)^2-\left(4x\right)^2=\left(x^2+4x+8\right)\left(x^2-4x+8\right).\)
c) \(64x^2+4y^4=4\left(16x^2+y^4\right)\)
d) \(x^5+x-1\)đa thức này có nghiệm vô tỷ. Mik ko phân tích được.
a) ax - 2x - a2 + 2a
= ( ax - 2x ) - ( a2 - 2a )
= x ( a - 2 ) - a ( a - 2 )
= ( a - 2 ) ( x - a )
b) x2 + x - ax - a
= ( x2 + x ) - ( ax + a )
= x ( x + 1 ) - a ( x + 1 )
= ( x + 1 ) ( x - a )
Hok Tốt!!!
a) ax -2x- a2+ 2a
= (ax -2x ) -(a2 -2a )
= x(a-2) -a ( a-2 )
= (x-a) (a-2)
b) x2 +x -ax -a
=( x2 +x ) - ( ax +a )
= x( x+1 ) -a ( x+1 )
= ( x-a ) (x+ 1)
c) 2x2 +4ax +x +2a
=( 2x2 + 4ax ) + ( x+ 2a )
= 2x ( x+ 2a ) + ( x+2a )
= ( 2x +1 ) (x+2a )
d) 2xy -ax +x2 - 2ay
= (2xy -2ay ) + ( -ax + x2 )
= 2y( x-a ) + x ( x-a)
= ( 2y +x ) ( x -a )
a,\(5ab-45a^3b\)
=\(5ab\left(1-9a^2\right)\)
=\(5ab\left(1-3a\right)\left(1+3a\right)\)
b,\(3a-6ab+5-10b\)
=\(\left(3a-6ab\right)+\left(5-10b\right)\)
=\(3a\left(1-2b\right)+5\left(1-2b\right)\)
=\(\left(1-2b\right)\left(3a+5\right)\)
c,\(a^2-7ab-2a+14b\)
=\(\left(a^2-7ab\right)-\left(2a-14b\right)\)
=\(a\left(a-7b\right)-2\left(a-7b\right)\)
=\(\left(a-7b\right)\left(a-2\right)\)
d,\(4a^2-8b+4a-8ab\)
=\(\left(4a^2-8ab\right)+\left(4a-8b\right)\)
=\(4a\left(a-2b\right)+4\left(a-2b\right)\)
=\(\left(a-2b\right)\left(4a+4\right)\)
=\(4\left(a-2b\right)\left(a+1\right)\)
e,\(a^2-5a+15b-9b^2\)
=\(\left(a^2-9b^2\right)-\left(5a-15b\right)\)
=\(\left(a-3b\right)\left(a+3b\right)-5\left(a-3b\right)\)
=\(\left(a-3b\right)\left(a+3b-5\right)\)