Question

1. phân tích thành nhân tử :
d) a² ( b - c ) + b² ( c - a) + c² ( a - b)
2. Thu gọn phân thức
\(\dfrac{a^2-b^2+4b-4}{2a-2b+4}\)
gấp ạ !

Answer 1

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

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

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

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

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

\(2.\dfrac{a^2-b^2+4b-4}{2a-2b+4}\)

\(=\dfrac{a^2-\left(b-2\right)^2}{2\left(a-b+2\right)}\)

\(=\dfrac{\left(a-b+2\right)\left(a+b-2\right)}{2\left(a-b+2\right)}\)

\(=\dfrac{a+b-2}{2}\)