Question

chứng tỏ

a)  a(b-c)-a(b+d)=-a(c+d)

b)   (a+b)(c+d)-(a+d)(b+c)=(a-c)(d-b)

Answer 1

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

b)  \(VT=\left(a+b\right)\left(c+d\right)-\left(a+d\right)\left(b+c\right)=ac+ad+bc+bd-ab-ac-bd-dc\)

\(=ad+bc-ab-dc=a\left(d-b\right)-c\left(d-b\right)=\left(d-b\right)\left(a-c\right)=VP\)

p/s: chúc bạn học tốt

Answer 2

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

=> ĐPCM

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

= a.(c+d)+b(c+d)-[a(b+c)+d(b+c)]

= ac+ad+bc+bd-(ab+ac+bd+cd)

= ac+ad+bc+bd-ab-ac-bd-cd

= ad+bc-ab-cd

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

= (a-c)(d-b)

=> ĐPCM

Answer 3

a) - Biến đổi VT: a(b-c)-a(b+d) = ab - ac - ab - ad = (ab-ab) - ac - ad = 0 - a.(c+d) = -a(c+d)

=> đ p c m

b) - Biến đổi VT = (a+b).(c+d) - (a+d).(b+c) = a.(c+d) + b.(c+d) - a.(b+c) - d.(b+c) = ac + ad + bc+bd - ab - ac - db - dc

= (ac-ac) + (bd - db) + ad - ab + bc - dc = a.(d-b) + c.(b-d) = -a.(b-d) + c.(b-d) =  (b-d).(-a+c) = (d-b).(a-c)

=> đ p c m