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PK
1
TH
1
15 tháng 10 2015
4a2=4b2-4a+1
=(2a)2-2*2a*1+12-4b2= (2a-1)2-(2b)2(2a-1-2b)(2a-1+2b)
18 tháng 10 2018
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) \(5a^3-10a^2b+5ab^2-10a+10b\)
\(=5a\left(a^2-2ab+b^2\right)-10\left(a-b\right)\)
\(=5a\left(a-b\right)^2-10\left(a-b\right)\)
\(=\left(a-b\right)\left[5a\left(a-b\right)-10\right]\)
\(=5\left(a-b\right)\left[a\left(a-b\right)-2\right]\)
\(=5\left(a-b\right)\left(a^2-ab-2\right)\)
18 tháng 10 2018
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
LT
26 tháng 8 2020
Phối hợp cả 3 phương phép để phân tích các đa thức sau thành phân tử:
a) 36 - 4a2 + 20ab - 25b2
= 36 - (4a2 - 20ab + 25b2)
= 62 - (2a - 5b)2
= (6 - 2a + 5b)(6 + 2a - 5b)
b) a3 + 3a2 + 3a + 1 - 27b3
= (a + 1)3 - (3b)3
= (a + 1 - 3b)[(a + 1)2 + 3b(a + 1) + 9b2]
= (a + 1 - 3b)(a2 + 2a + 1 + 3ab + 3b + 9b2)
c) x2 + 2xy + y2 - xz - yz
= (x + y)2 - z(x + y)
= (x + y)(x + y - z)
d) 5a3 - 10a2b + 5ab2 - 10a + 10b
= 5(a3 - 2a2b + ab2 - 2a + 2b)
= 5[a(a2 - 2ab + b2) - 2(a - b)]
= 5[a(a - b)2 - 2(a - b)]
= 5(a - b)(a2 - ab - 2)
19 tháng 8 2018
\(a.5a^3-10a^2b+5ab^2-10a+10b=5a\left(a^2-2ab+b^2\right)-10\left(a-b\right)=5a\left(a-b\right)^2-10\left(a-b\right)=5\left(a-b\right)\left(a^2-ab-2\right)\)
\(b.3x^3+6x^2y+3xy^2-12xz^2=3x\left(x^2+2xy+y^2-4z^2\right)=3x\left[\left(x+y\right)^2-4z^2\right]=3x\left(x+y+2z\right)\left(x+y-2z\right)\)
\(c.x^3+4xy^2-3x^2-6xy+4x^2y=x\left(x^2+4y^2-3x-6y+4xy\right)=4\left[\left(x+2y\right)^2-3\left(x+2y\right)\right]=4\left(x+2y\right)\left(x+2y-3\right)\)
\(d.12x^3-12x^2y+3xy^2-27xz^2=3x\left(4x^2-4xy+y^2-9z^2\right)=3x\left[\left(2x-y\right)^2-9z^2\right]=3x\left(2x-y-3z\right)\left(2x-y+3z\right)\)
NN
1
LT
24 tháng 8 2020
Bài 1:
a) x3 - 3x2 + 3x - 1 + 2(x2 - x)
= (x - 1)3 + 2x(x - 1)
= (x - 1)[(x - 1)2 + 2x]
= (x - 1)(x2 - 2x + 1 + 2x)
= (x - 1)(x2 + 1)
b) 36 - 4a2 + 20ab - 25b2
= 36 - (2a - 5b)2
= (6 - 2a + 5b)(6 + 2a - 5b)
c) 5a3 - 10a2b + 5ab2 - 10a + 10b
= 5(a3 - 2a2b + ab2 - 2a + 2b)
= 5[a(a2 - 2ab + b2) - 2(a - b)]
= 5[a(a - b)2 - 2(a - b)]
= 5(a - b)(a2 - ab - 2)
24 tháng 10 2020
a) ax + ay - bx - by = ( ax - bx ) + ( ay - by ) = x( a - b ) + y( a - b ) = ( a - b )( x + y ) < đã sửa >
b) 2x2 - 6xy + 5x - 15y = 2x( x - 3y ) + 5( x - 3y ) = ( x - 3y )( 2x + 5 )
c) ( a + b )2 - 4a2 = ( a + b )2 - ( 2a )2 = ( a + b - 2a )( a + b + 2a ) = ( b - a )( b + 3a )
d) 5a2xy - 10a3x - 15a2x2 = 5a2x( y - 2a - 3x )
e) 3( x - 1 ) + 5x( x - 1 ) = ( x - 1 )( 3 + 5x )
f) 9a2 - 4 = ( 3a )2 - 22 = ( 3a - 2 )( 3a + 2 )
g) 2x3 + 8x4 + 8x = 2x( x + 4x2 + 4 )
h) a2 - 4 + 4b - b2 = a2 - ( b2 - 4b + 4 ) = a2 - ( b - 2 )2 = ( a - b + 2 )( a + b - 2 )
i) a2 + 2ab + b2 - 16 = ( a2 + 2ab + b2 ) - 16 = ( a + b )2 - 42 = ( a + b - 4 )( a + b + 4 )
k) x2 + 5x + 4 = x2 + x + 4x + 4 = x( x + 1 ) + 4( x + 1 ) = ( x + 1 )( x + 4 )
l) 2x2 - 3x - 5 = 2x2 + 2x - 5x - 5 = 2x( x + 1 ) - 5( x + 1 ) = ( x + 1 )( 2x - 5 )
m) x3 + 6x2 + 9x = x( x2 + 6x + 9 ) = x( x + 3 )2
\(5a^3-10a^2b+5ab^2-10a+10b\)
\(=5a\left(a^2-2ab+b^2\right)-5\left(2a-2b\right)\)
\(=5a\left(a-b\right)^2-5\left(2a-2b\right)\)
\(=5\left[a\left(a-b\right)^2-\left(2a-2b\right)\right]\)
\(=5\left[a\left(a-b\right)^2-2\left(a-b\right)\right]\)
\(=5\left(a-b\right)\left[a\left(a-b\right)-2\right]\)
\(x^6-x^4+2x^3+2x^2\)
\(=x^4\left(x^2-1\right)+2x^2\left(x+1\right)\)
\(=x^4\left(x-1\right)\left(x+1\right)+2x^2\left(x+1\right)\)
\(=\left[x^4\left(x-1\right)+2x^2\right]\left(x+1\right)\)
\(=\left[x^5-x^4+2x^2\right]\left(x+1\right)\)
\(=x^2\left(x^3-x^2+2\right)\left(x+1\right)\)
5a3-10a2b+5ab2-10a+10b
=5a.(a2-2ab+b2) - 10.(a-b)
=5a.(a-b)2-10.(a-b)
=5(a-b).[a.(a-b) - 2]
x6-x4+2x3+2x2
= x4.(x2-1)+2x2.( x+1)
= x4.(x+1).(x-1) +2x2.(x+1)
= x2.(x+1).[x2.(x-1) + 2]
= x2.(x+1).(x3-x2+2)