Thu gọn biểu thức: a. (a – b – d) + (b – a + d)
b. – (a – b + c) – (a – b – c)
c. (c – a + d) + (a – b – d)
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a) A = ( a+ b – c + d ) – ( - a – b + c – d )
= a+ b – c + d + a + b - c + d
= 2a + 2b + 2d – 2c
b) B = ( a+ b – c ) + ( a – b ) – ( a – b - c )
= a+ b – c + a – b – a + b + c
= a + b
A = ( a+ b – c + d ) – ( - a – b + c – d )
= a+ b – c + d + a + b - c + d
= 2a + 2b + 2d – 2c
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) \(\left(a-b-d\right)+\left(b-a-d\right)=a-b-d+b-a-d\)
\(=\left(a-a\right)-\left(b-b\right)-\left(d+d\right)\)
\(=0-2d\)
\(=-2d\)
b) \(-\left(a-b+c\right)-\left(a-b-c\right)=-a+b-c-a+b+c\)
\(=\left(-a-a\right)+\left(b+b\right)-\left(c-c\right)\)
\(=-2a+2b\)
c) \(\left(c-a+d\right)+\left(a-b-d\right)=c-a+d+a-b-d\)
\(=c-\left(a-a\right)+\left(d-d\right)-b\)
\(=c-b\)
a ) \(\left(a-b-d\right)+\left(b-a-d\right)=a-b-d+b-a-d=-2d\)
b ) \(-\left(a-b+c\right)-\left(a-b-c\right)=-a+b-c-a+b+c=-2a+2b=2\left(-a+b\right)\)
c ) \(\left(c-a+d\right)+\left(a-b-d\right)=c-a+d+a-b-d=c-b\)
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: \(=\left(a+b\right)^2-\left(c+d\right)^2\)
b: \(=\left(a-d\right)^2-\left(b-c\right)^2\)
c: \(=\left(x+3z\right)^2-4y^2\)
d: \(=\left(a^2-9\right)\left(a^2+9\right)=a^4-81\)
e: \(=\left(a-5\right)^2\cdot\left(a+5\right)^2=\left(a^2-25\right)^2\)
a: =a-b-d+b-a+d=0