Rút gọn biểu thức: (a-b+c+d)(a-b-c-d)
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Rút gọn biểu thức
A= (a-b-c-d) + ( b-c+d-a)
\(A=\left(a-b-c-d\right)+\left(b-c+d-a\right)\)
\(=a-b-c-d+b-c+d-a\)
\(=-2c\)
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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
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(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
\(\left(a+b\right)\left(c+d\right)-\left(a+d\right)\left(b+c\right)\)
\(=ac+ad+bc+bd-ab-ac-db-dc\)
\(=ad+bc-ab-dc\)
\(=\left(ad-ab\right)+\left(bc-dc\right)\)
\(=a\left(d-b\right)+c\left(b-d\right)\)
\(=a\left(d-b\right)-c\left(d-b\right)\)
\(=\left(a-c\right)\left(d-b\right)\)
Rút gọn biểu thức sau:
(a+b)+(a-c-d+b)
7 tháng 6 2021 lúc 9:45
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
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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
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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
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Xem thêm câu trả lời
Rút gọn biểu thức
- ( a - b - c ) + ( b - c + d) - ( -a + b + d)
\(\text{- ( a - b - c ) + ( b - c + d) - ( -a + b + d) }\)
\(=-a+b+c+b-c+d+a-b-d\)
\(=\left(-a+a\right)+\left(b+b-b\right)+\left(c-c\right)+\left(d-d\right)\)
\(=0+b+0+0\)
\(=b\)
Bỏ dấu ngoặc rồi rút gọn biểu thức sau
a,(a+b) (c+d)-(a+d) (b+c)
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
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
\(\left[\left(a+b\right)+\left(c+d\right)\right]^2=\left(a+b\right)^2+2\left(a+b\right)\left(c+d\right)+\left(c+d\right)^2\)
\(\left[\left(a+b\right)-\left(c+d\right)\right]^2=\left(a+b\right)^2-2\left(a+b\right)\left(c+d\right)+\left(c+d\right)^2\)
\(\left[\left(a-b\right)+\left(c-d\right)\right]^2=\left(a-b\right)^2+2\left(a-b\right)\left(c-d\right)+\left(c-d\right)^2\)
\(\left[\left(a-b\right)-\left(c-d\right)\right]^2=\left(a-b\right)^2-2\left(a-b\right)\left(c-d\right)+\left(c-d\right)^2\)
\(A=2\left(a+b\right)^2+2\left(a-b\right)^2+2\left(c+d\right)^2+2\left(c-d\right)^2\)
\(A=2\left(a^2+2ab+b^2+a^2-2ab+b^2+c^2+2cd+d^2+c^2-2cd+d^2\right)\)
\(A=4\left(a^2+b^2+c^2+d^2\right)\)
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Rút gọn biểu thức
bc(a+d)(b-c)- ac(b+d)(a-c)+ ab(c+d)(a-b)
Cám ơn các bạn!
rút gọn biểu thức sau
D = (a + b - c) - (a - b + c) + (b + c - a) - ( a - b - c)
các bạn giải giùm mình nhé
\(D=\left(a+b-c\right)-\left(a-b+c\right)+\left(b+c-a\right)-\left(a-b-c\right)\)
\(D=a+b-c-a+b-c+b+c-a-a+b+c\)
\(D=\left(a-a-a-a\right)+\left(b+b+b+b\right)+\left(c+c-c-c\right)\)
\(D=4b-3a\)
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