Question

Phân tích:
a, \(x^4+2x^3-6x-9\)
b, \(4a^2b^2-\left(a^2+b^2-1\right)^2\)
c,\(\left(xy+4\right)^2-\left(2x+2y\right)^2\)
d, \(\left(a^2+b^2+ab\right)^2-a^2b^2-b^2c^2-c^2a^2\)

Answer 1

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

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

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

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

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

\(=\left[x\left(y-2\right)-2\left(y-2\right)\right]\left[x\left(y+2\right)+2\left(y+2\right)\right]\)

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