Question

bài 1:

a)(xy+1)^2-(x+y)^2

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

c)a(b^2-c^2)-b(a^2-c^2)+c(a^2-b^2)

Answer 1

a: \(\left(xy+1\right)^2-\left(x+y\right)^2\)

\(=\left(xy+1-x-y\right)\left(xy+1+x+y\right)\)

\(=\left[x\left(y-1\right)-\left(y-1\right)\right]\left[x\left(y+1\right)+\left(y+1\right)\right]\)

\(=\left(y-1\right)\left(x-1\right)\left(y+1\right)\left(x+1\right)\)

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

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

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

\(=2\left(a+b+c\right)\left(a+b-c\right)\)