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a2 -2ab+2b+b2-2a=(a2-2ab+b2)-(2a-2b)=(a-b)2-2(a-b)=(a-b)(a-b-2)
a^2 + b^2 - 2a + 2b - 2ab
= (a^2 - 2ab + b^2) - 2(a - b)
= (a - b)^2 - 2(a - b)
= (a - b)(a - b - 2)
a^2+b^2-2a+2b-2ab
=(a^2+b^2-2ab)-(2a-2b)
=(a-b)^2-2(a-b)
=(a-b)(a-b-2)
\(\Leftrightarrow\left(a+b\right)^2+2\left(a+b\right)+1=\left(a+b+1\right)^2\)
\(a^2+b^2+2a-2b-2ab=a^2-2ab+b^2+2\left(a-b\right)\)
\(=\left(a-b\right)^2+2\left(a-b\right)\)
\(=\left(a-b\right)\left(a-b+2\right)\)
\(4a^2-4b^2-4a+1=4a^2-4a+1-\left(2b\right)^2\)
\(=\left(2a-1\right)^2-\left(2b\right)^2\)
\(=\left(2a-1-2b\right)\left(2a-1+2b\right)\)
a2 + b2 + 2ab + 2a + 2b + 1
= ( a2 + 2ab + b2 ) + ( 2a + 2b ) + 1
= ( a + b )2 + 2( a + b ) + 12
= ( a + b + 1 )2
3x( x - 2y ) - 6y( 2y - x )
= 3x( x - 2y ) + 6y( x - 2y )
= 3( x - 2y )( x + 2y )
x2 + 2x - 3
= x2 - x + 3x - 3
= x( x - 1 ) + 3( x - 1 )
= ( x - 1 )( x + 3 )
a) \(a^2+b^2+2ab+2a+2b+1\)
\(=\left(a^2+2ab+b^2\right)+\left(2a+2b\right)+1\)
\(=\left(a+b\right)^2+2\left(a+b\right)+1\)
\(=\left(a+b+1\right)^2\)
b) \(3x\left(x-2y\right)-6y\left(2y-x\right)\)
\(=3x\left(x-2y\right)+6y\left(x-2y\right)\)
\(=3\left(x-2y\right)\left(x+2y\right)\)
c) \(x^2+2x-3=x^2-x+3x-3\)
\(=\left(x^2-x\right)+\left(3x-3\right)\)
\(=x\left(x-1\right)+3\left(x-1\right)\)
\(=\left(x-1\right)\left(x+3\right)\)
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)
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)
2a3-2ab2=2a(a2-b2)=2a(a+b)(a-b)
\(2a^3-2ab^2=2a\left(a^2-b^2\right)=2a\left(a+b\right)\left(a-b\right)\)
Chúc bạn học tốt ^_^