a) - ( - a + c – d ) – ( c – a + d ) 

= a - c - d - c + a + d

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

= 2a - 2c               

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

= - a - b + c - d + a - b - c - d

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

= -2b - 2d

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

= a - c + d - c + a - d 

= 2a

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

= - a-b+c-d+a-b-c-d

=-2d -2b

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

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

= ab-ac-ad-ab-ac+ad

= -2ab-2ac

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

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

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

=ad+bc-ab-cd

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

= a - c + d - c + a - d 

= 2a

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

= - a-b+c-d+a-b-c-d

=-2d -2b

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

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

= ab-ac-ad-ab-ac+ad

= -2ab-2ac

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

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

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

=ad+bc-ab-cd

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

= ac-ad+bc-bd-ac-ad+bc+bd

= 2bc-2ad

f) ( a + b )² – ( a – b )²

= a²+2ab+b² - (a²+2ab-b²)

=a²+2ab+b² - a²-2ab+b²

=2b²

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

b, - ( a+b-c+d) + (a-b-c-d) = -a -b+c-d + a-b-c-d = -2b + (-2c)= -2(b+c)

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

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

\(=-2c\)

giải hẳn ra giùm mik vs

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

\(D=a+b-c-a+b-c+b+c-a-a+b+c\)

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

\(D=4b-3a\)

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

Ta có

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

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

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

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

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

\(A=2\left(a^2+2ab+b^2+a^2-2ab+b^2+c^2+2cd+d^2+c^2-2cd+d^2\right)\)

\(A=4\left(a^2+b^2+c^2+d^2\right)\)

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

=(-c-b).d+b.c+b^2

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

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

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

=0+0+a.(d-b)+c.(b-d)

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

Hok tốt

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

\(=ac+ad+bc+bd-ab-ac-db-dc\)

\(=ad+bc-ab-dc\)

\(=\left(ad-ab\right)+\left(bc-dc\right)\)

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

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

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

a) -(-a + c - d) - (c - a + d) = a - c + d - c + a - d = (a + a) - (c + c) + (d - d) = 2a - 2c

b) -(a + b - c + d) + (a - b - c - d) = -a - b + c - d + a  - b - c - d = (-a + a) - (b + b) + (c - c) - (d + d) = -2b - 2d

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

d) (b + a) + (c - d) - (c + a) - (b - d) = b + a + c - d - c - a - b + d = (b - b) + (a - a) + (c - c) - (d - d) = 0

e) (a - b) - (d + a) - (c - d) + (c + b) = a - b - d - a - c + d +  c + b = (a - a) - (b - b) - (d - d) - (c - c) = 0

f) -a + (c - b) - (c + a - b) = - a + c - b - c - a + b = (-a - a) + (c - c) - (b - b) = -2a

a ) a - c + d - c + a - d = 2a - 2c 

b )  -a - b + c - d + a - b - c - d = -2b - 2d 

 CÁC CÂU CÒN LẠI LÀM TƯƠNG TỰ NHÉ!!

a) - ( -a + c - d ) - ( c - a + d ) = a - c + d - c + a - d = ( a + a ) - ( c + c ) + ( d - d ) = 2a - 2c = 2 ( a - c )

b) - ( a + b - c + d ) + ( a - b - c - d ) = -a - b + c - d + a - b - c - d = ( -a + a ) - ( b + b ) + ( c - c ) - ( d - d ) = -2b

c) ( a + b - c ) - ( b - c + d ) = a + b - c - b + c - d = a + ( b + b ) - ( c - c ) - d = a + 2b -d

d) ( b + a ) + ( c - d ) - ( c + a ) - ( b - d ) = b + a + c - d - c - a - b + d = ( b - b ) + ( a - a ) + ( c - c ) - ( d - d ) = 0

e) ( a - b ) - ( d + a ) - ( c - d ) + ( c + b ) = a - b - d - a - c + d + c + b = ( a - a ) - ( b - b ) - ( d - d ) - ( c - c ) = 0

f) -a + ( c - b ) - ( c + a - b ) = -a + c - b - c - a + b = ( -a - a ) + ( c - c ) - ( b - b ) = -2a

=))

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

2) \(=ac-ad+bc-bd-ac-ad+bc+bd=2bc-2ad=2\left(bc-ad\right)\)

3) \(\left(a+b\right)\left(a+b\right)-\left(a-b\right)\left(a-b\right)=a^2+2ab+b^2-a^2+2ab-b^2=4ab\)