Question

Phân tích đa thức sau thành nhân tử :

\(a,x^2-y^2-2x+2y\)

\(b,3a^2-6ab+3b^2-12c^2\)

\(c,x^2-25+y^2+2xy\)

Answer 1

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

\(=\left(x-1\right)^2-\left(y-1\right)^2=\left(x-1+y-1\right)\left(x-1-y+1\right)\)

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

b)\(3a^2-6ab+3b^2-12c^2=3\left(a^2-2ab+b^2-4c^2\right)\)\(=3\left[\left(a-b\right)^2-\left(2c\right)^2\right]\)

\(=3\left(a-b+2c\right)\left(a-b-2c\right)\)