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a) 7x – 14 = 7(x - 2)
b) 5x3 - 10x2y +5xy2 = 5x(x2 - 2xy - y2) = 5x(x - y)2
c) 25 – x2= (x - 5)(x + 5)
a, \(7\left(x-2\right)\)
c, \(\left(5-x\right)\left(5+x\right)\)
a, 7x - 14
= 7(x-2)
b, 2x - 2y + \(x^2\)- xy
= (2x-2y) + (\(x^2\)-xy)
= 2(x-y) + x(x-y)
= (x-y)(2+x)
c, 6x + 12
= 6(x+2)
\(a,=7\left(x-2\right)\\ b,=2\left(x-y\right)+x\left(x-y\right)=\left(x+2\right)\left(x-y\right)\\ c,=6\left(x+2\right)\\ d,\text{Sai đề}\)
\(a,10x^2y-20xy^2=10xy\left(x-2y\right)\\ b,x^2-y^2+10y-25=x^2-\left(y^2-10y+25\right)=x^2-\left(y-5\right)^2=\left(x-y+5\right)\left(x+y-5\right)\\ c,x^2-y^2+3x-3y=\left(x-y\right)\left(x+y\right)+3\left(x-y\right)=\left(x-y\right)\left(x+y+3\right)\\ d,x^3+3x^2-16x-48=\left(x^3+3x^2\right)-\left(16x+48\right)=x^2\left(x+3\right)-16\left(x+3\right)=\left(x+3\right)\left(x^2-16\right)=\left(x+3\right)\left(x+4\right)\left(x-4\right)\)
\(e,9x^3+6x^2+x=x\left(9x^2+6x+1\right)=x\left(3x+1\right)^2\\ f,x^4+5x^3+15x-9=\left(x^4+5x^3-3x^2\right)+\left(3x^2+15x-9\right)=x^2\left(x^2+5x-3\right)+3\left(x^2+5x-3\right)=\left(x^2+3\right)\left(x^2+5x-3\right)\)
a) \(=\left(6x\right)^2-2.6x.1+1=\left(6x-1\right)^2\)
b) \(=5xy\left(x^2+2x+1\right)=5xy\left(x+1\right)^2\)
c) \(=\left(3x-y\right)^2-25=\left(3x-y-5\right)\left(3x-y+5\right)\)
d) \(=x\left(x+1\right)+7\left(x+1\right)=\left(x+1\right)\left(x+7\right)\)
\(=5x\left(x^2-2xy+y^2\right)\)
\(=5x\left(x-y\right)^2\)
a/ \(=5x\left(x^2-2x+3\right)\)
b/ \(=\left(x^2-2x\right)-\left(x-2\right)=x\left(x-2\right)-\left(x-2\right)=\left(x-1\right)\left(x-2\right)\)
a) \(5x^3-10x^2+15x=5x\left(x^2-2x+3\right)\)
b) \(x^2-3x+2=x\left(x-1\right)-2\left(x-1\right)=\left(x-1\right)\left(x-2\right)\)
\(a,=\left(x-2\right)\left(9x^2y^2-6x^3y^2\right)=3x^2y^2\left(3-2x\right)\left(x-2\right)\\ b,=5x\left(x^2-y^2\right)+20x\left(x+y\right)=5x\left(x-y\right)\left(x+y\right)+20x\left(x+y\right)\\ =5\left(x+y\right)\left(x^2-xy+4x\right)\\ c,=8x^2+2x-12x-3=2x\left(4x+1\right)-3\left(4x+1\right)=\left(2x-3\right)\left(4x+1\right)\)
a, \(x^2-5x+6=x^2+x-6x+6=x\left(x-1\right)-6\left(x-1\right)=\left(x-1\right)\left(x-6\right)\)
b, \(3x^2+9x-30=3\left(x^2+3x-10\right)=3\left(x^2-2x+5x-10\right)\)
\(=3\left[x\left(x-2\right)+5\left(x-2\right)\right]=3\left(x-2\right)\left(x+5\right)\)
c, \(x^2+7x+10=x^2+2x+5x+10=x\left(x+2\right)+5\left(x+2\right)=\left(x+2\right)\left(x+5\right)\)
\(A=x^2-y^2+7x+7y\)
\(=\left(x-y\right)\left(x+y\right)+7\left(x+y\right)\)
\(=\left(x+y\right)\left(x-y+7\right)\)
\(B=4x^3-4x^2+x\)
\(=x\left(4x^2-4x+1\right)\)
\(=x\left(2x-1\right)^2\)
\(C=x^2-6xy+9y^2-9\)
\(=\left(x-3y\right)^2-9\)
\(=\left(x-3y-3\right)\left(x-3y+3\right)\)
A=\(x^2+7x+7y-y^2=\left(x^2-y^2\right)+\left(7x+7y\right)=\left(x-y\right)\left(x+y\right)+7\left(x+y\right)=\left(x+y\right)\left(x-y+7\right)\)
B=\(4x^3-4x^2+x=x\left(4x^2-4x+1\right)=x\left(2x-1\right)^2\)
C=\(x^2+9y^2-9-6xy=\left(x^2-6xy+9y^2\right)-9=\left(x-3y\right)^2-3^2=\left(x-3y-3\right)\left(x-3y+3\right)\)
a, 7x - 14 = 7 ( x - 2 )
b, 5x3 - 10x2y + 5xy2
= 5x ( x2 - 2xy + y2 )
= 5x ( x - y )2
c, 25 - x2 = 52 - x2 = ( 5 - x ) ( 5 + x )