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a,\(xy+3x-7y-21\)
\(=x\left(y+3\right)-7\left(y+3\right)\)
\(=\left(y+3\right)\left(x-7\right)\)
\(b,2xy-15-6x+5y\)
\(=\left(2xy-6x\right)+\left(-15+5y\right)\)
\(=2x\left(y-3\right)-5\left(3-y\right)\)
\(=2x\left(y-3\right)+5\left(y-3\right)\)
\(=\left(y-3\right)\left(2x+5\right)\)
a) 3x2 - 7x + 2
= 3x2 - 6x - x + 2
= (3x2 - 6x) - (x - 2)
= 3x (x - 2) - (x - 2)
= (3x - 1) (x - 2)
a) Ta có: \(-3x^2\left(2x^2-\frac{1}{3}x+2\right)\)
\(=-6x^4+x^3-6x^2\)
b) Ta có: \(2xy^2\left(x-3y+xy\right)\)
\(=2x^2y^2-6xy^3+2x^2y^3\)
c) Ta có: \(\left(5x^2-4x\right)\left(x-2\right)\)
\(=5x^3-10x^2-4x^2+8x\)
\(=5x^3-14x^2+8x\)
d) Ta có: \(-\left(2-x\right)\left(2x+3\right)\)
\(=\left(x-2\right)\left(2x+3\right)\)
\(=2x^2+3x-4x-6\)
\(=2x^2-x-6\)
e) Ta có: \(\left(3x^3-2x^2+x\right):\left(-2x\right)\)
\(=\frac{-3}{2}x^2+x-\frac{1}{2}\)
f) Ta có: \(\left(15x^2y^2-21x^3y+2x^2y\right):\left(3x^2y\right)\)
\(=5y-7x+\frac{2}{3}\)
g) 
\(3x\left(x-5\right)-x\left(4+3x\right)=43\)
\(\Leftrightarrow3x^2-15x-4x-3x^2=43\)
\(\Leftrightarrow-19x=43\)
\(\Leftrightarrow x=\frac{-43}{19}\)
a) x2( x - 1 ) - x + 1
= x2( x - 1 ) - ( x - 1 )
= ( x - 1 )( x2 - 1 )
= ( x - 1 )( x - 1 )( x + 1 )
= ( x - 1 )2( x + 1 )
b) ( a + b )3 - ( a - b )3
= ( a3 + 3a2b + 3ab2 + b3 ) - ( a3 - 3a2b + 3ab2 - b3 )
= a3 + 3a2b + 3ab2 + b3 - a3 + 3a2b - 3ab2 + b3
= 6a2b + 2b3
= 2b( 3a2 + b )
c) 6x( x - 3 ) + 9 - 3x2
= 6x2 - 18x + 9 - 3x2
= 3x2 - 18x + 9
= 3( x2 - 6x + 3 )
d) x( x - y ) - 5x + 5y
= x( x - y ) - ( 5x - 5y )
= x( x - y ) - 5( x - y )
= ( x - y )( x - 5 )
e) 3( x + 4 ) - x2 - 4x
= 3( x + 4 ) - ( x2 + 4x )
= 3( x + 4 ) - x( x + 4 )
= ( x + 4 )( 3 - x )
f) x2 + 4x - y2 + 4
= ( x2 + 4x + 4 ) - y2
= ( x + 2 )2 - y2
= ( x + 2 - y )( x + 2 + y )
g) x2 + 5x
= x( x + 5 )
h) -x2 + 2x + 2y + y2
= ( y2 - x2 ) + ( 2x + 2y )
= ( y - x )( y + x ) + 2( x + y )
= ( x + y )( y - x + 2 )
\(a,2x^2-4xy+2y^2-8t^2\)
\(=2\left[\left(x^2-2xy+y^2\right)-4t^2\right]\)
\(=2\left[\left(x-y\right)^2-\left(2t^2\right)\right]-\)
\(=2\left(x-y+2t\right)\left(x-y-2t\right)\)
\(b,x^3+x+3x^2y+2xy^2+y^3+y\)
\(=\left(x^3+3x^2y+3xy^2+y^3\right)+\left(x+y\right)\)
\(=\left(x+y\right)^3+\left(x+y\right)\)
\(=\left(x+y\right)\left[\left(x+y\right)^2+1\right]\)
\(=\left(x+y\right)\left(x^2+2xy+y^2+1\right)\)
\(c,x^4-7x^2=x^2\left(x^2-7\right)\)
\(=x^2\left(x+\sqrt{7}\right)\left(x-\sqrt{7}\right)\)
Sửa đề:\(d,5x-5y-x^2+2xy-y^2\)
\(=5\left(x-y\right)-\left(x-y\right)^2\)
\(=\left(x-y\right)\left(5-x+y\right)\)
\(e,x^4+4x^3+4x^2-x^2y^2\)
\(=\left(x^4+4x^3+4x^2\right)-x^2y^2\)
\(=\left(x^2+2x\right)^2-\left(xy\right)^2\)
\(=\left(x^2+2x+xy\right)\left(x^2+2x-xy\right)\)
\(g,x^2-y^2-2y-1\)
\(=x^2-\left(y+1\right)^2\)
\(=\left(x+y+1\right)\left(x-y-1\right)\)
a) \(2x^2-4xy+2y^2-8t^2=2\left(x^2-2xy+y^2-4t^2\right)\)
\(=2\left(\left(x-y\right)^2-\left(2t\right)^2\right)=2\left(x-y-2t\right)\left(x-y+2t\right)\)
b) \(x^3+x+3x^2y+3xy^2+y^3+y=\left(x^3+3x^2y+3xy^2+y^3\right)+\left(x+y\right)\)
\(=\left(x+y\right)^3+\left(x+y\right)=\left(x+y\right)^2\left(x+y\right)+\left(x+y\right)\)
\(=\left(x^2+2xy+y^2\right)\left(x+y\right)+\left(x+y\right)=\left(x^2+2xy+y^2+1\right)\left(x+y\right)\)
c) \(x^4-7x^2=\left(x^2\right)^2-\left(\sqrt{7}x\right)^2=\left(x^2-\sqrt{7}x\right)\left(x^2+\sqrt{7}x\right)\)
d) câu này hình như đề sai thì phải
e) \(x^4+4x^3+4x^2-x^2y^2=x^2\left(x^2+4x+4-y^2\right)\)
\(=x^2\left(\left(x+2\right)^2-y^2\right)=x^2\left(x+2-y\right)\left(x+2+y\right)\)
g) \(x^2-y^2-2y-1=x^2-\left(y^2+2y+1\right)=x^2-\left(y+1\right)^2\)
\(=\left(x-y-1\right)\left(x+y+1\right)\)
\(=x^3+x^2-\left(4x+4\right)=x^2\left(x+1\right)-4\left(x+1\right)=\left(x^2-4\right)\left(x+1\right)\)
\(=\left(x-2\right)\left(x+1\right)\left(x+2\right)\)
\(x^4+x^3+x^2-1=x^3\left(x+1\right)+\left(x-1\right)\left(x+1\right)=\left(x+1\right)\left(x^3+x-1\right)\)
\(c,=\left(x+y\right)^2-2\left(x+y\right)+1=\left(x+y-1\right)^2\)
\(d,=x^2y^2-y^2-x^2+1=\left(x^2-1\right)\left(y^2-1\right)=\left(x-1\right)\left(y-1\right)\left(x+1\right)\left(y+1\right)\)
\(e,4x^2+4x-15=\left(4x^2+4x+1\right)-16=\left(2x+1\right)^2-4^2=\left(2x+5\right)\left(2x-3\right)\)
\(3x^2-7x+2=\left(3x^2-6x\right)-\left(x-2\right)=3x\left(x-2\right)-\left(x-2\right)=\left(3x-1\right)\left(x-2\right)\)
\(4x^2-5x+1=\left(4x^2-4x\right)-\left(x-1\right)=4x\left(x-1\right)-\left(x-1\right)=\left(4x-1\right)\left(x-1\right)\)
Phân tích à :v
a) x3 + x2 - 4x - 4 = x2( x + 1 ) - 4( x + 1 ) = ( x + 1 )( x2 - 4 ) = ( x + 1 )( x - 2 )( x + 2 )
b) x4 + x3 + x2 - 1 = x3( x + 1 ) + ( x - 1 )( x + 1 ) = ( x + 1 )( x3 + x - 1 )
c) x2 + 2xy + y2 - 2x - 2y + 1 = ( x2 + 2xy + y2 ) - ( 2x + 2y ) + 1 = ( x + y )2 - 2( x + y ) + 12 = ( x + y - 1 )2
d) x2y2 + 1 - x2 - y2 = ( x2y2 - x2 ) - ( y2 - 1 ) = x2( y2 - 1 ) - ( y2 - 1 ) = ( y2 - 1 )( x2 - 1 ) = ( y - 1 )( y + 1 )( x - 1 )( x + 1 )
e) 4x2 + 4x - 15 = ( 4x2 + 4x + 1 ) - 16 = ( 2x + 1 )2 - 42 = ( 2x + 1 - 4 )( 2x + 1 + 4 ) = ( 2x - 3 )( 2x + 5 )
g) 3x2 - 7x + 2 = 3x2 - 6x - x + 2 = 3x( x - 2 ) - ( x - 2 ) = ( x - 2 )( 3x - 1 )
h) 4x2 - 5x + 1 = 4x2 - 4x - x + 1 = 4x( x - 1 ) - ( x - 1 ) = ( x - 1 )( 4x - 1 )