x^2-2007x-2008
Phan tich da thuc thanh nhan tu
giup minh nha
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\(x^4-x+2008x^2+2008x+2008\)
\(=x\left(x^3-1\right)+2008\left(x^2+x+1\right)\)
\(=x\left(x-1\right)\left(x^2+x+1\right)+2008\left(x^2+x+1\right)\)
\(=\left(x^2+x+1\right)\left(x^2-x+2008\right)\)
\(x^4-x^2-56\)
\(=x^4-8x^2+7x^2-56\)
\(=x^2\left(x^2-8\right)+7\left(x^2-8\right)\)
\(=\left(x^2-8\right)\left(x^2+7\right)\)
\(\left(xy+1\right)^2-\left(x-y\right)^2=\left(xy+1+x-y\right)\left(xy+1-x+y\right)\)
\(=x^2y^2+xy-x^2y+xy^2+xy+1-x+y+x^2y+x-x^2+xy-xy^2-y+xy-y^2\)
\(=x^2y^2+2xy-x^2-y^2+1\)
\(=\left(x^2+x\right)^2+3\left(x^2+x\right)+2-12\)
\(=\left(x^2+x\right)^2+3\left(x^2+x\right)-10\)
\(=\left(x^2+x+5\right)\left(x^2+x-2\right)\)
\(=\left(x^2+x+5\right)\left(x+2\right)\left(x-1\right)\)
Ta có
a, x2-x-y2-y
=x2-y2-(x+y)
=(x-y)(x+y) - (x+y)
=(x+y)(x-y-1)
b, x2-2xy+y2-z2
=(x-y)2-z2
=(x-y-z)(x-y+z)
x^2 + 7x -15
= x^2 + 7x +12,25 -27,25
= (x+3,5)^2 - 27, 25
= ( x+3,5 - \(\sqrt{27,25}\))(x+3,5+\(\sqrt{27,25}\))
x 2 - 2007x - 2008
= x 2 + x - 2008x - 2008
= ( x 2 + x ) - ( 2008x + 2008 )
= x ( x + 1 ) - 2008 . ( x + 1 )
= ( x + 1 ) . ( x - 2008 )