Phân tích các đa thức sau thành nhân tử:
a) 10x2 ( x + y ) -10 ( x + y ) y2
b) ( x - 3 )2 - (2 - 3x )2
c) ( x + 1 )3 + ( x - 2 )3
d) x2 + 2xy + y2 - 4
e) 1 - y3 + 6xy2 - 12xy2+ 8x3
g) - 27 + 27x - 9x2 + x3
h) x3 - 2x2 - x + 2
i) x2 + xy - 7x - 7y
k) -6x2 - 5y + 3xy + 10x
l) x3 + y3 + 3y2 + 3y + 1
h) x²³-2x² − x + 2 i) x² + xy - FX-74: k) - 6x² - 5y + 3xy + 10x l) x² + y² + 3y² + 3y + 1
a: \(=10\left(x+y\right)\left(x^2-y^2\right)=10\left(x+y\right)^2\cdot\left(x-y\right)\)
b: \(=\left(x-3-2+3x\right)\left(x-3+2-3x\right)\)
\(=\left(4x-5\right)\left(-2x-1\right)\)
c: \(=\left(x+1+x-2\right)\left(x^2+2x+1-x^2+x+2+x^2-4x+4\right)\)
\(=\left(2x-1\right)\left(x^2-x+7\right)\)
d: \(=\left(x+y\right)^2-4=\left(x+y+2\right)\left(x+y-2\right)\)
\(e;=\)đề sai sửa \(12xy^2->12x^2y\Rightarrow e;=\left(2x-y+1\right)\left(4x^2-4xy-2x+y^2+y+1\right)\)
\(g;=\left(x-3\right)^3\)
\(i;=\left(x-7\right)\left(x+y\right)\)
\(k;=\left(3x-5\right)\left(y-2x\right)\)
\(l;=\left(x+y+1\right)\left(x^2-xy-x+y^2+2y+1\right)\)
\(h;=\left(x^2-1\right)\left(x^{21}+x^{19}+x^{17}+x^{15}+x^{13}+x^{11}+x^9+x^7+x^5+x^3+x-2\right)\)
\(i;Fx?\)
\(k;=\left(3x-5\right)\left(y-2x\right)\)
\(l;\) ko phân tích đc
g) \(x^3-9x^2+27x-27=x^3-3.3x^2+3.3^2.x-3^3=\left(x-3\right)^3\)
