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a) 3x2 - 15x3 = 3x2.( 1 - 5x )
b) x.( 2x - 3 ) + y.( 3 - 2x ) = x.( 2x - 3 ) - y.( 2x - 3 ) = ( 2x - 3 ).( x - y )
c) ( 5x - y )2 - 4x2 = ( 5x - y )2 - ( 2x )2 = ( 5x - y - 2x ).( 5x - y + 2x ) = ( 3x - y ).( 7x - y )
d) x2 - 9y2 + 4 - 4x = ( x2 - 4x + 4 ) - 9y2 = ( x - 2 )2 - ( 3y )2 = ( x - 2 - 3y ).( x - 2 + 3y )
\(65,x^3+8=\left(x+3\right)\left(x^2-3x+4\right)\)
\(87,x^3+9x^2+27x+27\)
\(=\left(x+3\right)^3\)
\(97,125-75m+15m^2-m^3\)
\(=\left(5-m\right)^3\)
TL:
\(a,1-2m+m^2-x^2-4x-4\)
\(=\left(m-1\right)^2-\left(x-2\right)^2\)
\(=\left(m+x-3\right)\left(m-x+1\right)\)
\(a.=x^3+3x^2y+3x^2y+9xy^2+3xy^2+9y^3\)
\(=x^2\left(x+3y\right)+3xy\left(x+3y\right)+3y^2\left(x+3y\right)\)
\(=\left(x+3y\right)\left(x^2+3xy+3y^2\right).\)
\(b.=9x^3+3x^2y+9x^2y+3xy^2+3xy^2+y^3\)
\(=3x^2\left(3x+y\right)+3xy\left(3x+y\right)+y^2\left(3x+y\right)\)
\(=\left(3x^2+3xy+y^2\right)\left(3x+y\right)\).
a) \(-4x^2+12xy-9y^2+25\)
\(=-\left(4x^2-12xy+9y^2\right)+25\)
\(=-\left[\left(2x\right)^2-2.2x.3y+\left(3y\right)^2\right]+25\)
\(=-\left(2x-3y\right)^2+25\)
\(=-\left(2x-3y\right)^2+5^2\)
\(=5^2-\left(2x-3y\right)^2\)
\(=\left(5-2x-3y\right)\left(5+2x-3y\right)\)
b) \(\left(3x-1\right)^2-16\)
\(=\left(3x-1\right)^2-4^2\)
\(=\left(3x-1-4\right)\left(3x-1+4\right)\)
\(=\left(3x-5\right)\left(3x+3\right)\)
a ) \(-4x^2+12xy-9y^2+25\)
\(=-\left(4x^2-12xy+9y^2-25\right)\)
\(=-\left[\left(2x-3y\right)^2-25\right]\)
\(=-\left(2x-3y+5\right)\left(2x-3y-5\right)\)
b ) \(\left(3x-1\right)^2-16\)
\(=\left(3x-1+4\right)\left(3x-1-4\right)\)
\(=\left(3x+3\right)\left(3x-5\right)\)
Bài làm:
\(8x^3+4x^2-9x+30=8x^3+16x^2-12x^2-24x+15x+30\)
\(=8x^2\left(x+2\right)-12x\left(x+2\right)+15\left(x+2\right)\)
\(=\left(x+2\right)\left(8x^2-12x+15\right)\)
\(8x^3+4x^2-9x+30\)
\(=8x^3+16x^2-12x^2-24x+15x+30\)
\(=8x^2\cdot\left(x+2\right)-12x\cdot\left(x+2\right)+15x\cdot\left(x+2\right)\)
\(=\left(x+2\right)\cdot\left(8x^2-12x+15\right)\)
\(25-4x^2+12xy-9y^2\)
\(=25-\left(2x-3y\right)^2\)
\(=\left(5-2x+3y\right)\left(5+2x-3y\right)\)