rút gọn biểu thức
a ) ( a - b + c + d ) - ( a - b ) + ( c - d )
b ) - ( a - b + c ) - ( a + b - c ) + ( - a + c )
Bỏ ngoặc rồi rút gọn biểu thức:
a) - ( - a + c – d ) – ( c – a + d ) ; b) – ( a + b - c + d ) + ( a – b – c –d )
c) a( b – c – d ) – a ( b + c – d ) ; d)(a+ b) ( c + d) – ( a + d ) ( b + c )
e)( a + b ) ( c – d ) – ( a – b ) ( c + d ) ; f) ( a + b ) 2 – ( a – b ) 2
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
Bỏ dấu ngoặc rồi rút gọn biểu thức.
a) (a+b)*(c+d)-(a+d)*(b+c)
b) (a+b)*(c-d)-(a-b)*(c+d)
c) (a+b)^2-(a-b)^2
Bài 1: bỏ dấu ngoặc rồi rút gọn biểu thức a, - ( - a + c - d ) - ( c - d + d) b, - ( a + b - c + d ) + (a - b - c - d) c, a( b - c - d ) - a( b + c -d ) d*, (a + b).(c+d) - ( a+d).(b+c) e*, (a+b).(c-d) - (a-b).(c+d) f*, (a+b)2 - (a-b)2
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)
Rút gọn biểu thức
A= (a-b-c-d) + ( b-c+d-a)
\(A=\left(a-b-c-d\right)+\left(b-c+d-a\right)\)
\(=a-b-c-d+b-c+d-a\)
\(=-2c\)
rút gọn biểu thức sau
D = (a + b - c) - (a - b + c) + (b + c - a) - ( a - b - c)
các bạn giải giùm mình nhé
\(D=\left(a+b-c\right)-\left(a-b+c\right)+\left(b+c-a\right)-\left(a-b-c\right)\)
\(D=a+b-c-a+b-c+b+c-a-a+b+c\)
\(D=\left(a-a-a-a\right)+\left(b+b+b+b\right)+\left(c+c-c-c\right)\)
\(D=4b-3a\)
bài 1 bỏ dấu ngoặc rồi rút gọn biểu thức a)-(-a+c-d) - (c-d+a) b)- (a+b-c+d) + (a-b-c-d) c)a(b-c-d)- a(b+c-d)
mng giáo viên hà ngọc thắng giải cho
Rút gọn biểu thức: A = (a+b+c+d)2+(a+b-c-d)2+(a+c-b-d)2+(a+d-b-c)2
\(A=\left[\left(a+b\right)+\left(c+d\right)\right]^2+\left[\left(a+b\right)-\left(c+d\right)\right]^2+\left[\left(a-b\right)+\left(c-d\right)\right]^2+\left[\left(a-b\right)-\left(c-d\right)\right]^2\)
Ta có
\(\left[\left(a+b\right)+\left(c+d\right)\right]^2=\left(a+b\right)^2+2\left(a+b\right)\left(c+d\right)+\left(c+d\right)^2\)
\(\left[\left(a+b\right)-\left(c+d\right)\right]^2=\left(a+b\right)^2-2\left(a+b\right)\left(c+d\right)+\left(c+d\right)^2\)
\(\left[\left(a-b\right)+\left(c-d\right)\right]^2=\left(a-b\right)^2+2\left(a-b\right)\left(c-d\right)+\left(c-d\right)^2\)
\(\left[\left(a-b\right)-\left(c-d\right)\right]^2=\left(a-b\right)^2-2\left(a-b\right)\left(c-d\right)+\left(c-d\right)^2\)
\(A=2\left(a+b\right)^2+2\left(a-b\right)^2+2\left(c+d\right)^2+2\left(c-d\right)^2\)
\(A=2\left(a^2+2ab+b^2+a^2-2ab+b^2+c^2+2cd+d^2+c^2-2cd+d^2\right)\)
\(A=4\left(a^2+b^2+c^2+d^2\right)\)
Rút gọn biểu thức
(a+b).(c+d)-(a+d).(b+c)
(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
\(\left(a+b\right)\left(c+d\right)-\left(a+d\right)\left(b+c\right)\)
\(=ac+ad+bc+bd-ab-ac-db-dc\)
\(=ad+bc-ab-dc\)
\(=\left(ad-ab\right)+\left(bc-dc\right)\)
\(=a\left(d-b\right)+c\left(b-d\right)\)
\(=a\left(d-b\right)-c\left(d-b\right)\)
\(=\left(a-c\right)\left(d-b\right)\)
Bỏ dấu ngoặc rồi rút gọn biểu thức:
a) - ( - a + c - d) - (c - a + d )
b) - (a + b - c + d) + ( a - b - c -d )
c) ( a + b - c ) - ( b - c + d)
d) ( b + a) + ( c - d) - (c +a ) - ( b - d)
e) ( a - b) - ( d + a) - (c - d) + ( c + b)
f) - a + ( c- b ) - (c + a - b)
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
=))
Bỏ dấu ngoặc rồi rút gọn biểu thức
(a+b).(c+d)-(a+d).(b+c)
(a+b).(c-d)-(a-b).(c+d)
(a+b)2-(a-b)2
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) \(\left(a+b\right)\left(a+b\right)-\left(a-b\right)\left(a-b\right)=a^2+2ab+b^2-a^2+2ab-b^2=4ab\)