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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
\(1.\)
\(x^2-2x+1-xy-y=\left(x-1\right)^2-y\left(x-1\right)=\left(x-1\right)\left(x-1-y\right)\)
\(2.\)
\(x^3-4x^2+4x-2x+2=x\left(x^2-4x+4\right)-2\left(x-1\right)=x\left(x-2\right)^2-2\left(x-1\right)\)
\(3.\)
\(10x-25-x^2+4y^2=4y^2-\left(x^2-10x+25\right)=4y^2-\left(x-5\right)^2=\left(2y+x-5\right)\left(2y-x+5\right)\)
\(4.\)
\(4x^2-2x+2xy-y=2x\left(2x-1\right)+y\left(2x-1\right)=\left(2x-1\right)\left(2x+y\right)\)
\(5.\)
\(4x\left(x-3\right)^2-3x^2+9x=4x\left(x-3\right)^2-3x\left(x-3\right)=\left(x-3\right)\left(4x^2-12x-3x\right)\)
a, \(=12x^5+9x^3y^2-6x^2y^3-20x^4y-15x^2y^3-10xy^4-24x^3y^2-18xy^4+12y^5\)
(tự rút gọn cái :P)
b, \(8x^3+4x^2y-2xy^2-y^3\)
\(=4x^2\left(2x+y\right)-y^2\left(2x+y\right)=\left(2x+y\right)^2\left(2x-y\right)\)
\(4x^2y^2-4x^2-4xy-y^2=4x^2y^2-\left(2x+y\right)^2\)
\(=\left(2x+y+2xy\right)\left(2xy-2x+y\right)\)
Mấy cái còn lại nhân tung ra là được mà :))))
\(x^3+4x^2+4x+3\)
\(=x^3+3x^2+x^2+3x+x+3\)
\(=x^2\left(x+3\right)+x\left(x+3\right)+\left(x+3\right)\)
\(=\left(x+3\right)\left(x^2+x+1\right)\)
\(x^2-y^2+4y-4\)
\(=x^2-\left(y^2-4y+4\right)\)
\(=x^2-\left(y-2\right)^2\)
\(=\left(x-y+2\right)\left(x+y-2\right)\)
\(x^4+x^3y-xy^3-y^4\)
\(=x^3\left(x+y\right)-y^3\left(x+y\right)\)
\(=\left(x+y\right)\left(x^3-y^3\right)\)
\(=\left(x+y\right)\left(x-y\right)\left(x^2+xy+y^2\right)\)
Chúc bạn học tốt.
\(a,6x^2-9x=3x\left(x-3\right)\)
\(b,x^3-2x^2-3x+6\)
\(=\left(x^3-2x^2\right)-\left(3x-6\right)\)
\(=x^2\left(x-2\right)-3\left(x-2\right)\)
\(=\left(x^2-3\right)\left(x-2\right)\)
\(e,2x\left(x-y\right)-3y\left(x-y\right)\)
\(=\left(2x-3y\right)\left(x-y\right)\)
a) 6x2 - 9x
= 3x (2x - 3)
b) x3 - 2x2 - 3x + 6
= x2(x - 2) - 3 (x - 2)
=(x - 2) (x2 - 3)
c) x2 - 4x + 4 - 9y2
= (x - 2)2 - 9y2
=(x - 2 - 3y)(x - 2 + 3y)
e) 2x(x - y) - 3y(x - y)
= (x - y)(2x - 3y)
xin lỗi mình học ngu nên không biết làm nhìu nha
\(x^2+4x-y^2+4\\ =\left(x^2+4x+4\right)-y^2\\ =\left(x+2\right)^2-y^2\\ =\left(x+2-y\right)\cdot\left(x+2+y\right)\)
\(2xy-x^2-y^2+16\\ =\left(x^2-2xy+y^2\right)-16\\ =\left(x-y\right)^2-16\\ =\left(x-y+4\right)\cdot\left(x-y-4\right)\)
\(x^2-2x-4y^2-4y\\ =\left(x^2-4y^2\right)-\left(2x+4y\right)\\ =\left(x-2y\right)\cdot\left(x+2y\right)-2\left(x+2y\right)\\ =\left(x+2y\right)\cdot\left(x-2y+2\right)\)
\(x^2+6x+9-y^2\\ =\left(x-3\right)^2-y^2\\ =\left(x-3-y\right)\cdot\left(x-3+y\right)\)
\(3x^2+6xy+3y^2-3z^2\\ =3\cdot\left(x^2+2xy+y^2-z^2\right)\\ =3\cdot\left[\left(x^2+2xy+y^2\right)-y^2\right]\\ =3\cdot\left[\left(x-y\right)^2-z^2\right]\\ =3\cdot\left(x-y-z\right)\cdot\left(x-y+z\right)\)
\(9x-x^3\\ =x\cdot\left(9-x^2\right)\\ =x\cdot\left(3-x\right)\cdot\left(3+x\right)\)
\(\left(2xy+1\right)^2-\left(2x+y\right)^2\\ =\left(2xy+1-2x-y\right)\cdot\left(2xy+1+2x-y\right)\)
Câu 2 nha
\(a,x^4+2x^3+x^2\)
\(=x^2\left(x^2+2x+1\right)\)
\(=x^2\left(x+1\right)^2\)
\(c,x^2-x+3x^2y+3xy^2+y^3-y\)
\(=\left(x^3+3x^2y+3xy^2+y^3\right)-\left(x+y\right)\)
\(=\left(x+y\right)^3-\left(x+y\right)\)
\(=\left(x+y\right)\left(x^2+2xy+y^2-1\right)\)
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,\(x^2-x-12\)
\(=x^2-4x+3x-12\)
\(=\left(x^2+3x\right)-\left(4x-12\right)\)
\(=x\left(x+3\right)-4\left(x+3\right)\)
\(=\left(x-4\right)\left(x+3\right)\)