Question

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

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

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

Answer 1

Đề chắc là chứng minh đẳng thức:

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

BL:

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

\(=ab-ac-ab-ad\)

\(=\left(ab-ab\right)-\left(ac+ad\right)\)

\(=-\left(ac+ad\right)\)

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

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

b) \(\left(a+b\right)\left(c+d\right)-\left(a+d\right)\left(b+c\right)=\left(a-c\right)\left(d-b\right)\) BL: \(\left(a+b\right)\left(c+d\right)-\left(a+d\right)\left(b+c\right)\) = \(ac+bc+ad+bd-ab+db-ac-dc\) Đến đây tự tách lấy, muộn rồi, phải i ngủ!!!