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phân tích đa thức thành nhân tử
a/x2(x+1)-2x(x+1)+(x+1)=(x+1)(x^2-2x+1)=(x+1)(x-1)^2
b/a2+b2+2a-2b-2ab=(a^2-ab)+(b^2-ab)+2(a-b)=a(a-b)-b(a-b)+2(a-b)=(a-b)(a-b+2)
c/ 4x2-8x+3=(2x-2)^2-1=(2x-2-1)(2x-2+1)=(2x-3)(2x-1)
d/25-16x2=5^2-(4x)^2=(5-4x)(5+4x)
1/ phân tích thành nhân tử ;
= C2-( a +b )2=( c-a -b ) . ( c+a +b )
mình chỉ làm được câu b) thôi ^^
a^2-2ab+b^2-4x^2
= (a-b)^2-(2x)^2
= (a-b+2x)(a-b-2x)
a/ x2+2x-y2+1=x2+2x+1-y2
= x2+x+x+1-y2
= x(x+1)+(x+1)-y2
= (x+1)2-y2
= (x+1-y)(x+1+y)
b/ a2-2ab+b2-4x2=a2-ab-ab+b2-(2x)2
=a(a-b)-b(a-b)-(2x)2
=(a-b)2-(2x)2
= (a-b-2x)(a-b+2x)
\(36x^2-9y^2-12x-6y\)
\(=\left(36x^2-12x+1\right)-\left(9y^2+6y+1\right)\)
\(=\left(6x-1\right)^2-\left(9y+1\right)\)
\(=\left(6x+9y\right)\left(6x-3y-2\right)\)
\(=3\left(2x+3y\right)\left(6x-3y-2\right)\)
a) a3 - a2c + a2b - abc
= a( a2 - ac + ab - bc )
= a[ a( a - c ) + b( a - c ) ]
= a( a - c )( a + b )
b) ( x2 + 1 )2 - 4x2
= ( x2 + 1 )2 - ( 2x )2
= ( x2 - 2x + 1 )( x2 + 2x + 1 )
= ( x - 1 )2( x + 1 )2
c) x2 - 10x - 9y2 + 25
= ( x2 - 10x + 25 ) - 9y2
= ( x - 5 )2 - ( 3y )2
= ( x - 3y - 5 )( x + 3y - 5 )
d) 4x2 - 36x + 56
= 4( x2 - 9x + 14 )
= 4( x2 - 7x - 2x + 14 )
= 4[ x( x - 7 ) - 2( x - 7 ) ]
= 4( x - 7 )( x - 2 )
a,\(a^3-a^2c+a^2b-abc\)
\(=a\left(a^2-ac+ab-bc\right)\)
\(=a\left[a\left(a-c\right)+b\left(a-c\right)\right]\)
\(=a\left(a-b\right)\left(a-c\right)\)
b,\(\left(x^2+1\right)^2-4x^2\)
\(=\left(x^2+1-2x\right)\left(x^2+1+2x\right)\)
\(=\left(x-1\right)^2\left(x+1\right)^2\)
c,\(x^2-10x-9y^2+25\)
\(=\left(x^2-10x+25\right)-9y^2\)
\(=\left(x-5\right)^2-\left(3y\right)^2\)
\(=\left(x-5-3y\right)\left(x-5+3y\right)\)
d,\(4x^2-36x+56\)
\(=4\left(x^2-9x+14\right)\)
\(=4\left(x^2-7x-2x+14\right)\)
\(=4\left(x-7\right)\left(x-2\right)\)
a) a2 + b2 + 2ab + 2a + 2b + 1
= (a2 + b2 + 2ab) + (2a + 2b) + 1
= (a + b)2 + 2(a + b) + 1
= (a + b + 1)2
b) a3 - 3a + 3b - b3
= (a3 - b3) - (3a - 3b)
= (a - b)(a2 - ab + b2) - 3(a - b)
= (a - b)(a2 - ab + b2 - 3)
c) x2 + 2x - 15
= (x2 + 2x + 1) - 16
= (x + 1)2 - 16
= (x + 1 - 5)(x + 1 + 5)
= (x - 4)(x + 6)
d) a4 + 6a2b + 9b2 - 1
= (a2 + 3b)2 - 1
= (a2 + 3b - 1)(a2 + 3b + 1)
a) \(x^3+2x^2+3x+2=x^3+x^2+x^2+x+2x+2=x^2\left(x+1\right)+x\left(x+1\right)+2\left(x+1\right)\)
\(=\left(x+1\right)\left(x^2+x+2\right)\)
b) \(=\left(x-y\right)^2-\left(a-b\right)^2=\left(x-y+a-b\right)\left(x-y-a+b\right)\)
a) x3+2x2+3x+2
= x3+x2+x2+x+2x+2
= x2(x+1)+x(x+1)+2(x+1)
= (x+1)(x2+x+2)
b) x2-2xy+y2-a2+2ab-b2
= (x2-2xy+y2)-(a2-2ab+b2)
= (x-y)2-(a-b)2
= (x-y+a-b)(x-y-a+b)
1) 36x2 - a2 + 10a - 25
= 36x2 - ( a2 - 10a + 25 )
= 36x2 - ( a - 5 )2
= ( 6x - a + 5)( 6x - a - 5)
2) x2 - 2x + 1 - a2 - 2ab - b2
= (x - 1)2 - ( a + b)2
= ( x - 1 - a - b)(x-1+a-b)
1) 36x2 - a2 +10a -25
= 36x2-(a2-10a+25)
=(6x)2 - (a-5)2
= (6x - a + 5)(6x+a-5)
2) x2-2x+1-a2-2ab-b2
= (x2-2x+1)-(a2-2ab-b2)
= (x-1)2 - (a-b)2
= (x-1-a+b)(x-1+a-b)