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1) \(=\left(2z+3\right)\left(4z^2-6z+9\right)\)
2) \(=\left(\frac{3x^2}{5}-\frac{1}{2}\right)\left(\frac{3x^2}{5}+\frac{1}{2}\right)\)
3) \(=\left(x-1\right)\left(x+1\right)\left(x^2+1\right)\left(x^4+1\right)\left(x^8+1\right)\left(x^{16}+1\right)\)
4) \(=\left(2x+1\right)^2\)
5) \(=\left(x-10\right)^2\)
6) \(=\left(y^2-7\right)^2\)
7) \(=\left(5x-4y\right)\left(25x^2+20xy+16y^2\right)\)
Bài 4.
a) 3xy2 - 45x2y = 3xy( y - 15x )
b) 25y2 - 4x2 + 4x - 1
= 25y2 - ( 4x2 - 4x + 1 )
= ( 5y )2 - ( 2x - 1 )2
= ( 5y - 2x + 1 )( 5y + 2x - 1 )
c) x2 - 5x + xy - 5y
= x( x - 5 ) + y( x - 5 )
= ( x - 5 )( x + y )
d) x2 - 8x - 33
= x2 + 3x - 11x - 33
= x( x + 3 ) - 11( x + 3 )
= ( x + 3 )( x - 11 )
Bài 5.
a) A = ( x - 2 )3 - x2( x - 4 ) + 8
= x3 - 6x2 + 12x - 8 - x3 + 4x2 + 8
= -2x2 + 12x
B = ( x2 - 6x + 9 ) : ( x - 3 ) - x( x + 7 ) - 9
= ( x - 3 )2 : ( x - 3 ) - x2 - 7x - 9
= x - 3 - x2 - 7x - 9
= -x2 - 6x - 12
b) Với x = -1 thì A = -2.(-1)2 + 12.(-1) = -2 - 12 = -14
Phân tích các đa thức sau thành nhân tử ... c) 6x(x+y)^2+3x^2y(x+y). 2: .... x3 - 5x + 8x - 4=x2 . x -5x + 8x -22 = (x2 - 22) . (x -5x + 8x )=(x-2) . (x+2) . 4x. x3 - 9x2 ..... Phân tích các đa thức sau thành nhân tử : a,x^3+5x^2+8x+4 b, x^3-9x^2+6x+16 .
\(x^2-4x+3=x^2-3x-x+3=x\left(x-3\right)-\left(x-3\right)=\left(x-1\right)\left(x-3\right)\)
\(x^2+5x+4=x^2+4x+x+4=x\left(x+4\right)+\left(x+4\right)=\left(x+1\right)\left(x+4\right)\)
\(x^2-x-6=x^2-3x+2x-6=x\left(x-3\right)+2\left(x-3\right)=\left(x+2\right)\left(x-3\right)\)
\(x^4+4=\left(x^2\right)^2+2.x^2.2+2^2-4x^2=\left(x^2+2\right)^2-4x^2=\left(x^2+2\right)^2-\left(2x^2\right)=\left(x^2+2+2x\right)\left(x^2-2-2x\right)\)
b) \(-4x^2-4x-1\)
\(=-\left(4x^2+4x+1\right)\)
\(=-\left(2x+1\right)^2\)
c) \(\frac{4}{9}x^2-25y^2\)
\(=\left(\frac{2}{3}x+5y\right)\left(\frac{2}{3}x-5y\right)\)
d) \(\frac{1}{27}x^3-8\)
\(=\left(\frac{1}{3}x-2\right)\left(\frac{1}{9}x+\frac{2}{3}x+4\right)\)
`a, 4x^2 - 25y^2 = (2x-5y)(2x+5y)`.
`b, 8x^3 +27 = (2x+3)(4x^2 - 6x + 9)`.
`c, 125x^3 - 64y^3 = (5x)^3 - (4y)^3 = (5x-4y)(25x^2 + 20xy + 16y^2)`.
\(a,\\ 4x^2-25y^2=\left(2x\right)^2-\left(5y\right)^2=\left(2x-5y\right)\left(2x+5y\right)\\ b,\\ 8x^3+27=\left(2x\right)^3+3^3=\left(2x+3\right)\left(4x^2+6x+9\right)\\ c,\\ 125x^3-64y^3=\left(5x\right)^3-\left(4y\right)^3=\left(5x-4y\right)\left(25x^2+20xy+16y^2\right)\)