Question

Phân tích các đa thức thành nhân tử:

a. x⁶-y⁶

b.x³⁵+x³⁴+x³³+.......+x²+x+1

c.x²-6xy+9y²-9

e.(x-9)(x-7)+1

Answer 1

a.x\(^6\)-y\(^6\)=(x\(^2\))\(^3\)+(y\(^2\))\(^3\) =(x\(^2\)+y\(^2\))(x\(^4\)-x\(^2\)y\(^2\)+y\(^4\))

b.x\(^{35}\)+x\(^{34}\)+......+x+1 =x\(^{34}\).(x+1)+......+(x+1)

=(x\(^{34}\)+x\(^{32}\)+......+x\(^2\)+1)(x+1)

c.x\(^2\)-6xy+9y\(^2\)-9 =x\(^2\)-2.3xy+(3y)\(^2\)-3\(^2\) =(x-3y)\(^2\)-3\(^2\)

=(x-3y-3)(x-3y+3)

d.(x-9)(x-7)+1 =x\(^2\)-7x-9x+63+1 =x\(^2\)-16x+64

=x\(^2\)-2.8x+8\(^2\) =(x-8)\(^2\)