Question

Phân tích đa thức thành nhân tử

a, x⁴-4x³+4x²

^​b, 2ab^​2​-a²b-b³

^​c, x²y²+1-x²-y²

d, x⁴-x²+2x-1

​e, x^​3+3x²-3x-1

​f, x^​3-3x²-3x+1

​g, x³-4x²​+4x-1

​h, 4a²b²-(a²+b²-1)²

​i, (xy+4)²​-(2x+2y)²

​k, (a²+b²​+ab)^​2-a²b²-b²c²-c²a²

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Answer 1

a) x⁴-4x³+4x²

⁼ x²(x²-4x+4)

= x²(x-2)²

b) 2ab²-a²b-b³

= -b(-2ab+a²+b²)

=-b(a-b)²

Answer 2

e) x³+3x²-3x-1

= x³-x²+4x²-4x+x-1

=(x³-x²)+(4x²-4x)+(x-1)

=x²(x-1)+4x(x-1)+(x-1)

(x-1)(x²+4x+1)

f) x³-3x²-3x+1

=x³+x²-4x²-4x+x+1

=(x³+x²)-(4x²+4x)+(x+1)

=x²(x+1)-4x(x+1)+(x+1)

=(x+1)(x²-4x+1)

g)x³-4x²+4x-1

=x³-x²-3x²+3x+x-1

=(x³-x²)-(3x²-3x)+(x-1)

=x²(x-1)-3x(x-1)+(x-1)

=(x-1)(x²-3x+1)