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1: \(=2x^2\left(7x-2\right)\)
2: \(=5y^6\left(y^4+3\right)\)
3: \(=3xy\left(3xy-5x-7y\right)\)
4: \(=\left(x+1\right)\left(3x^2-2\right)\)
5: \(=\left(a+b+c\right)\left(a+b+c-ab-bc-ca-1\right)\)
6: \(=4x^2\left(x-2y\right)+20x\left(x-2y\right)\)
\(=4x\left(x-2y\right)\left(x+5\right)\)
7: \(=3x^2y\left(a-b+c\right)-2xy\left(a-b+c\right)\)
\(=xy\left(a-b+c\right)\left(3x-2\right)\)
a, 4x3 -12x2 + 9x
=x(4x2 -12x + 9)
=x((2x)2 - 2.3.2x + 32)
=x(2x - 3)2
b,ab + c2 -ac - bc
=(ab - ac) + (c2 - bc)
=a(b - c) + c(c - b)
=a(b - c) - c(b - c)
=(a - c)(b - c)
c,4x2 - y2 + 1 - 4x
=((2x)2 - 2.2x + 1) - y2
=(2x - 1)2 - y2
=(2x - y -1)(2x + y - 1)
d,6x2 - 7x - 20
= -(-6x2 + 7x + 20)
= -(-6x2 + 11x +10 + 10 - 4x)
= -((3x + 2)(-2x + 5) + 10 - 4x)
= -(3x + 2)(-2x + 5) -10 + 4x
= -(3x + 2)(-2x + 5) - 2(-2x + 5)
= -(-2x + 5)(3x + 4)
\(A=\left(6x-3y\right)+\left(4x^2-4xy+y^2\right)\)
\(=3\left(2x-y\right)+\left(2x-y\right)^2\)
\(=\left(3+2x-y\right)\left(2x-y\right)\)
\(B=9x^2-\left(y^2-4y+4\right)\)
\(=9x^2-\left(y-2\right)^2\)
\(=\left(3x+y-2\right)\left(3x-y+2\right)\)
A = ( 6x - 3y ) + (4x2 - 4xy + y2 )
A = 3.( 2x - y) + [ ( 2x )2 - 2.2.x.y + y2 ]
A = 3.( 2x - y ) + ( 2x - y )2
A = ( 2x - y ).(3 + 2x - y )
B = 9x2 - ( y2 - 4y + 4 )
B = ( 3x )2 - ( y - 2 )2
B = ( 3x - y + 2 ).( 3x + y - 2 )
C = - 25x2 + y2 - 6y + 9
C = ( y2 - 2.3.y + 32 ) - ( 5x )2
C = ( y - 3 )2 - ( 5x )2
C = (y - 3 - 5x ).( y - 3 +5x )
D = x2 - 4x - y2 -- 8y - 12
D = ( x2 - 4x + 4 ) - 4 - y2 - 8y -12
D = ( x - 2.2x + 22 ) - ( y2 + 2.4.y + 42 )
D = ( x - 2 )2 - ( y + 4 )2
D = ( x - 2 + y + 4 ).( x - 2 - y - 4 )
D = ( x + y + 2 ).( x - y - 6 )
\(a)\) \(3x^2-6x=3x\left(x-2\right)\)
\(b)\) \(9x^3-9x^2y-4x+4y\)
\(=9x^2.\left(x-y\right)-4\left(x-y\right)\)
\(=\left(9x^2-4\right)\left(x-y\right)\)
\(=[\left(3x\right)^2-2^2]\left(x-y\right)\)
\(=\left(3x-2\right)\left(3x+2\right)\left(x-y\right)\)
\(c)\) \(x^3-2x^2-8x\)
\(=x\left(x^2-2x-8\right)\)
\(=x\left(x+2\right)\left(x-4\right)\)
\(b,2x^2+4x+2-2y^2\)
\(=2\left(x^2+2x+1-y^2\right)\)
\(=2\left[\left(x+1\right)^2-y^2\right]\)
\(=2\left(x+1+y\right)\left(x+1-y\right)\)
\(a,6x^3-9x^2=3x^2\left(2x-3\right)\)
\(b,4x^2y-8xy^2+10x^2y^2=2xy\left(2x-4y+5xy\right)\)
\(c,20x^2y-12x^3=4x^2\left(5y-3x\right)\)
\(d,4xy^2+8xyz=4xy\left(y+2z\right)\)
b, x2 + 9x - 10
= x2 + 10x - x -10
= ( x2 - x ) +(10x - 10)
=x( x - 1) + 10 ( x - 1)
= ( x - 1)(x + 10 )
\(x\left(9xy^2-4\right)\)
9x2y2-4x
= x(9xy2−4)