Question

chứng minh 

a) (x+a) (x + b) = x² + (a+b) x +ab

b) (x+a) (x+b) (x+x) = x³ + (a+b+c) x² + (ab+bc+ca) x +abc

Answer 1

P/s : Phần b ) : \(\left(x+a\right)\left(x+b\right)\left(x+c\right)\)

a )   \(\left(x+a\right)\left(x+b\right)=x^2+ax+bx+ab=x^2+\left(a+b\right)x+ab\)

b )   \(\left(x+a\right)\left(x+b\right)\left(x+c\right)\) 

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

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

\(=x^3+x^2c+\left(ax+bx\right)\left(x+c\right)+abx+abc\)

\(=x^3+x^2c+ax^2+bx^2+axc+bxc+abx+abc\)

\(=x^3+\left(x^2a+x^2b+x^2c\right)+\left(abx+bcx+axc\right)+abc\)

\(=x^3+\left(a+b+c\right)x^2+\left(ab+bc+ca\right)x+abc\)