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Phân tích các đa thức sau thành nhân tử :
a) x - y + 5x - 5y
= ( x + 5x ) - ( y + 5y )
= x . ( 1 + 6 ) - y . ( 1 + 6 )
= ( 1 + 6 ) . ( x - y )
\(a,x-y+5x-5y=\left(x-y\right)+5\left(x-y\right)=6\left(x-y\right)\)
\(3x\left(x-5\right)-x\left(4+3x\right)=43\)
\(\Leftrightarrow3x^2-15x-4x-3x^2=43\)
\(\Leftrightarrow-19x=43\)
\(\Leftrightarrow x=\frac{-43}{19}\)
A = xy + y - 2x - 2
= y( x + 1 ) - 2( x + 1 )
= ( x + 1 )( y - 2 )
B = x2 - 3x + xy - 3y
= x( x - 3 ) + y( x - 3 )
= ( x - 3 )( x + y )
C = 3x2 - 3xy - 5x + 5y
= 3x( x - y ) - 5( x - y )
= ( x - y )( 3x - 5 )
D = xy + 1 + x + y
= y( x + 1 ) + ( x + 1 )
= ( x + 1 )( y + 1 )
E = ax - bx + ab - x2
= ( ax - x2 ) + ( ab - bx )
= x( a - x ) + b( a - x )
= ( a - x )( x + b )
F = x2 + ab + ax + bx
= ( ax + x2 ) + ( ab + bx )
= x( a + x ) + b( a + x )
= ( a + x )( x + b )
G = a3 - a2x - ay + xy
= a2( a - x ) - y( a - x )
= ( a - x )( a2 - y )
Bonus : = ( a - x )[ a2 - ( √y )2 ]
= ( a - x )( a - √y )( a + √y )
H = 2xy + 3z + 6y + xz
= ( 6y + 2xy ) + ( 3z + xz )
= 2y( 3 + x ) + z( 3 + x )
= ( 3 + x )( 2y + z )
A = xy + y - 2x - 2 = y(x + 1) - 2(x + 1) = (y - 2)(x + !1
B = x2 - 3x + xy - 3y = x(x - 3) + y(x - 3) = (x + y)(x - 3)
C = 3x2 - 3xy - 5x + 5y = 3x(x - y) - 5(x - y) = (3x - 5)(x - y)
D = xy + 1 + x + y = xy + x + y + 1 = x(y + 1) + (y + 1) = (x + 1)(y + 1)
E = ax - bx + ab - x2 = ax - x2 + ab - bx = a(a - x) - b(a - x) = (a - b)(a - x)
F = x2 + ab + ax + bx = ab + ax + bx + x2 = a(b + x) + x(b + x) = (a + x)(b + x)
G = a3 - a2x - ay + xy = a2(a - x) - y(a - x) = (a2 - y)(a - x)
H = 2xy + 3z + 6y + xz = 2xy + 6y + 3z + xz = 2y(x + 3) + z(x + 3) = (2y + z)(x + 3)
1, <=> \(\left(4x\right)^2-\left(9y\right)^2\)=\(\left(4x-9y\right)\left(4x+9y\right)\)
1) \(16x^2-81.y^2=\left(4x\right)^2-\left(9.y\right)^2=\left(4x-9y\right)\left(4x+9y\right)\)
2) \(\left(5x-3y\right)^2-\left(3x-5y\right)^2=\left(5x-3y-3x+5y\right)\left(5x-3y+3x-5y\right)=\left(2x+2y\right).\left(8x-8y\right)\)
\(=16.\left(x+y\right)\left(x-y\right)\)
3)\(4x^2-y^2+4y-4=4x^2-\left(y^2-4y+4\right)=\left(2x\right)^2-\left(y-2\right)^2=\left(2x-y+2\right).\left(2x+y-2\right)\)
4)\(9.\left(x-y\right)^2-16.\left(2x+y\right)^2=3^2.\left(x-y\right)^2-4^2.\left(2x+y\right)^2=\left(3x-3y\right)^2-\left(8x+4y\right)^2\)
\(=\left(3x-3y-8x-4y\right)\left(3x-3y+8x+4y\right)=\left(-5x-7y\right).\left(11x+y\right)\)
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) (x2 + xy) - (5x + 5y) = x(x + y) - 5(x + y)
= (x + y)(x - 5)
b) (2x - x +2 )(2x + x - 2) = (x + 2)(x - 2)
d) 2x2 + 2x - 7x - 7 = (2x2 + 2x) - (7x + 7)
= 2x(x + 1) - 7(x + 1) = (x + 1)(2x - 7)
c) 3(16x2y2 - y2 + 2xy - x2)
= 3\(\left[16x^2y^2-\left(y^2-2xy+x^2\right)\right]\)
= 3\(\left[16x^2y^2-\left(y-x\right)^2\right]\)
= 3(4xy - y + x)(4xy + y - x)