Question

Bài 1 : Khai triển và thu gọn

a) (a+b)(a-b)-a²+b²

b) (-a+b)(a-b)+a²+b²

c) a.(b+c)-b.(c-a)+c.(b-a)

d) (a+b)(c+d)-(a-b)(c-d)

 

Answer 1

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

\(=a^2-b^2-a^2+b^2=0\)

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

\(=-a^2+2ab-b^2+a^2+b^2=2ab\)

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

\(=ab+ac+ab-bc+bc-ac\)

\(=ab+ab=2ab\)

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

\(=ac+ad+bc+bd-ac+ad+bc-bd\)

\(=2ad+2bc=2\left(ad+bc\right)\)