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Câu 2 nha
\(a,x^4+2x^3+x^2\)
\(=x^2\left(x^2+2x+1\right)\)
\(=x^2\left(x+1\right)^2\)
\(c,x^2-x+3x^2y+3xy^2+y^3-y\)
\(=\left(x^3+3x^2y+3xy^2+y^3\right)-\left(x+y\right)\)
\(=\left(x+y\right)^3-\left(x+y\right)\)
\(=\left(x+y\right)\left(x^2+2xy+y^2-1\right)\)
\(x^3+8y^3+2xy^2+x^2y\)
\(=x^3+2x^2y-x^2y-2xy^2+4xy^2+8y^3\)
\(=x^2\left(x+2y\right)-xy\left(x+2y\right)+4y^2\left(x+2y\right)\)
\(=\left(x+2y\right)\left(x^2-xy+4y^2\right)\)
1. x2 - 16 - 4xy + 4y2
= ( x2 - 4xy + 4y2 ) - 16
= ( x - 2y )2 - 42
= ( x - 2y - 4 )( x - 2y + 4 )
2. 4x2 + 4x - 3
= ( 4x2 + 4x + 1 ) - 4
= ( 2x + 1 )2 - 2
= ( 2x + 1 - 2 )( 2x + 1 + 2 )
= ( 2x - 1 )( 2x + 3 )
3. x2 - x - 12
= x2 + 3x - 4x - 12
= x( x + 3 ) - 4( x + 3 )
= ( x + 3 )( x - 4 )
4. 3x + 3y - x2 - 2xy - y2
= ( 3x + 3y ) - ( x2 + 2xy + y2 )
= 3( x + y ) - ( x + y )2
= ( x + y )( 3 - x - y )
5. 4y4 + 16
= 4( y4 + 4 )
= 4( y4 + 4y2 + 4 - 4y2 )
= 4[ ( y4 + 4y2 + 4 ) - 4y2 ]
= 4[ ( y2 + 2 )2 - ( 2y )2 ]
= 4( y2 - 2y + 2 )( y2 + 2y + 2 )
a,\(x^2-16-4xy+4y^2\)
\(=\left(x^2-4xy+4y^2\right)-16\)
\(=\left(x-2y\right)^2-4^2\)
\(=\left(x-2y-4\right)\left(x-2y+4\right)\)
b,\(4x^2+4x-3\)
\(=4x^2-2x+6x-3\)
\(=\left(4x^2-2x\right)+\left(6x-3\right)\)
\(=2x\left(2x-1\right)+3\left(2x-1\right)\)
\(=\left(2x+3\right)\left(2x-1\right)\)
c,\(x^2-x-12\)
\(=x^2-4x+3x-12\)
\(=\left(x^2+3x\right)-\left(4x-12\right)\)
\(=x\left(x+3\right)-4\left(x+3\right)\)
\(=\left(x-4\right)\left(x+3\right)\)
\(\left(2x+1\right)^2-\left(x-1\right)^2\)
\(\Leftrightarrow\left(2x+1-x+1\right)\left(2x+1+x-1\right)\)
\(\Leftrightarrow\left(x+2\right)3x\)
A . 5(x-y)-y(x-y)
=(x6-y)(5-y)
B . x^2 - xy - 8x+8y
=(x^2-xy)-(8x-8y))
=x(x-y) - 8(x-y)
C. x^2-10x+25 - y^2
=(x^2 - 10x + 25 ) - y^2
=(x-5)^2 - y^2
=(x-5+y)(x-5-y)
D . x^3 - 3x^2-4x+12
=(x^3 - 3x^2 ) - (4x - 12)
=x^2 (x-3)-4(x-3)
=(x^2-4)(x-3)
=(x+2)(x-2)(x-3)
D . 2x^2-2y^2- 6x-6y
=(2^x - 2y^2) - (6x+ 6y)
=2(x^2 - y^2) - 6(x+y)
=2(x+y)(x-y) - 6(x+y)
=2(x+y)(x-y-3)
E . x^3 - 3x^2 + 3x - 1
=(x-1)^3
D.x^2+3x+2
=x^2+2x+x+2
=(x^2+2x)+(x+2)
=x(x+2)+(x+2)
=(x+2)(x+1)
\(1.\)
\(x^2-2x+1-xy-y=\left(x-1\right)^2-y\left(x-1\right)=\left(x-1\right)\left(x-1-y\right)\)
\(2.\)
\(x^3-4x^2+4x-2x+2=x\left(x^2-4x+4\right)-2\left(x-1\right)=x\left(x-2\right)^2-2\left(x-1\right)\)
\(3.\)
\(10x-25-x^2+4y^2=4y^2-\left(x^2-10x+25\right)=4y^2-\left(x-5\right)^2=\left(2y+x-5\right)\left(2y-x+5\right)\)
\(4.\)
\(4x^2-2x+2xy-y=2x\left(2x-1\right)+y\left(2x-1\right)=\left(2x-1\right)\left(2x+y\right)\)
\(5.\)
\(4x\left(x-3\right)^2-3x^2+9x=4x\left(x-3\right)^2-3x\left(x-3\right)=\left(x-3\right)\left(4x^2-12x-3x\right)\)
x4-3x3-x+3 = (x4-3x3)-(x-3) = x3(x-3)-(x-3) = (x-3)(x3-1) = (x-3)(x-1)(x2+x+1)
3x+3y-x2-2xy-y2 = (3x+3y)-(x2+2xy+y2) = 3(x+y)-(x+y)2 = (x+y)( 3-x-y)
x2-x-12 = x(x-1)-12
4x4+ 4x2y2- 8y4
<=> (2x2- 2y2)