Question

phân tích đa thức thành nhân tử:

a)4a^2b^2-(a^2+b^2-1)^2

b)(xy+4)^2-(2x+2y)^2

c)x^4-2x^3-6x-9

d)x^4-2x^3+x^2-1

e)(a+1)(a^2-1)-(a-1)(a^2+1)

f)(ab-1)^2-(a-2)^2

Answer 1

a) \(4a^2b^2-\left(a^2+b^2-1\right)^2\)

\(=\left(2ab\right)^2-\left(a^2+b^2-1\right)^2\)

\(=\left(2ab-a^2-b^2+1\right)\left(2ab+a^2+b^2-1\right)\)

\(=\left(1-a^2+2ab-b^2\right)\left(a^2+2ab+b^2-1\right)\)

\(=\left[1-\left(a-b\right)^2\right]\left[\left(a+b\right)^2-1\right]\)

\(=\left(1-a+b\right)\left(1+a-b\right)\left(a+b-1\right)\left(a+b+1\right)\)

b) \(\left(xy+4\right)^2-\left(2x+2y\right)^2\)

\(=\left(xy+4-2x-2y\right)\left(xy+4+2x+2y\right)\)

Answer 2

c)x⁴-2x³-6x-9

=(x4-9)-(2x3+6x)

=(x²+3)(x²-3)-2x(x²-3)

=(x²-3)(x²+3-2x)

Answer 3

(ab-1)²-(a-2)²

=(ab-1-a+2)(ab-1+a-2)

=(ab-a+1)(ab+a-3)