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a) \(\left(a+b\right)\left(c+d\right)-\left(a+d\right)\left(b+c\right)\)
\(=ac+ad+bc+bd-ab-ac-db-dc\)
\(=ad+bc-dc-ab\)
\(=d\left(a-c\right)-b\left(a-c\right)\)
\(=\left(a-c\right)\left(d-b\right)\)
b) \(\left(a+b\right)\left(c-d\right)-\left(a-b\right)\left(c+d\right)\)
\(=ac-ad+bc-bd-ac-ad+bc+bd\)
\(=2bc-2ad\)
\(=2\left(bc-ad\right)\)
c) \(\left(a+b\right)^2-\left(a-b\right)^2\)
\(=\left(a+b\right)\left(a+b\right)-\left(a-b\right)\left(a-b\right)\)
\(=a^2+2ab+b^2-a^2+2ab-b^2\)
\(=4ab\)
Bài 1:
a) Ta có: (a-b)+(c-d)-(a+c)
=a-b+c-d-a-c
=-b-d(1)
Ta lại có: -(b+d)=-b-d(2)
Từ (1) và (2) suy ra (a-b)+(c-d)-(a+c)=-(b+d)
b) Ta có: (a-b)-(c-d)+(b+c)
=a-b-c+d+b+c
=a+d(đpcm)
c) Ta có: a(b-c)-b(a-c)
=ab-ac-ab+cb
=cb-ca
=c(b-a)(đpcm)
d) Ta có: b(c-a)+a(b-c)
=bc-ba+ab-ac
=bc-ac
=c(b-a)(đpcm)
e) Ta có: -c(-a+b)+b(c-a)
=ca-cb+bc-ba
=ca-ba
=a(c-b)(đpcm)
g) Ta có: a(c-b)-b(-a-c)
=ac-ab+ba+bc
=ac+bc
=c(a+b)(đpcm)
d) \(\left(2x+1\right)^3=\left(2x+1\right)^2\)
\(\Rightarrow\left(2x+1\right)^3-\left(2x+1\right)^2=0\)
\(\Rightarrow\left(2x+1\right)^2\left[1-\left(2x+1\right)\right]=0\)
\(\Rightarrow\left(2x+1\right)^2=0\) hoặc \(1-\left(2x+1\right)=0\)
+) \(\left(2x+1\right)^2=0\)
\(\Rightarrow2x+1=0\)
\(\Rightarrow x=\frac{1}{2}\) ( không thỏa mãn )
+) \(1-\left(2x+1\right)=0\)
\(\Rightarrow2x+1=1\)
\(\Rightarrow x=0\) ( thỏa mãn )
Vậy x = 0
Bài 1: Thực hiện phép tính
a) 165 - [ 120 - ( 9 - 4 )2 ]
b) 32 : { 160 : [ 300 - ( 175 + 21 . 5 ) ] }
c) 6 . 52 - 32 : 24 + 32
d) 42 .37 - 42 . 33 + 24
Bài làm:
a) 165 - [ 120 - ( 9 - 4 )2 ]
= 165 - [ 120 - 52 ]
= 165 - [ 120 - 25 ]
= 165 - 95
= 70.
b) 32 : { 160 : [ 300 - ( 175 + 21 . 5 ) ] }
= 32 : { 160 : [ 300 - ( 175 + 105) ] }
= 32 : { 160 : [ 300 - 280 ] }
= 32 : { 160 : 20 }
= 32 : 8
= 4.
c) 6 . 52 - 32 : 24 + 32
= 6 . 25 - 32 : 16 + 9
= 150 - 2 + 9
= 148 + 9
= 157.
d) 42 .37 - 42 . 33 + 24
= 16. ( 37 - 33)
= 16 . 4
= 64.
Bài 2: Tìm số tự nhiên x, biết:
a) 91-5 . ( 5 + x ) = 61
b) ( x + 34 ) - 40 = 28
c) 3 . ( x -2 ) + 150 = 240
d) 360 : ( x- 7) = 90
e) 2448 : [ 119 - ( x - 6) ] = 24.
Bài làm:
a) 91-5 . ( 5 + x ) = 61
5 . ( 5 + x) = 91 - 61
5. ( 5+ x) = 30
5 +x = 30 : 5
5 +x = 6
x = 6 - 5
x = 1.
b) ( x + 34 ) - 40 = 28
x+ 34 = 40 + 28
x+ 34 = 68
x = 68 - 34
x = 34.
c) 3 . ( x - 2 ) + 150 = 240
3 . ( x - 2 ) = 240 - 150
3 . ( x - 2 ) = 90
x - 2 = 90 : 3
x - 2 = 30
x = 30 + 2
x = 32.
d) 360 : ( x - 7 ) = 90
x - 7 = 360 : 90
x - 7 = 4
x = 4 + 7
x = 11.
e) 2448 : [ 119 - ( x - 6 ) ] = 24
[ 119 - ( x - 6 ) ] = 2448 : 24
[ 119 - ( x - 6 ) ] = 102
x - 6 = 119 + 102
x - 6 = 221
x = 221 + 6
x = 227.
********************************Chúc bạn học tốt***********************************
B1:a )
(x-4).(y+3)=-3=-1.3=-3.1
ta có bảng sau:
| x-4 | -1 | 3 |
| x | 3 | 1 |
| y+3 | 3 | 1 |
| y | 0 | -2 |
Câu 2:
\(2\cdot S=2+2^2+...+2^{2018}\)
=>\(S=2^{2018}-1\)
\(5\cdot2^{2017}>2\cdot2^{2017}=2^{2018}>2^{2018}-1\)
nên \(B< 5\cdot2^{2017}\)
a)\(\left(a+b\right)\left(a-b\right)-a^2+b^2\)
\(=a^2-b^2-a^2+b^2=0\)
b)\(\left(-a+b\right)\left(a-b\right)+a^2+b^2\)
\(=-a^2+2ab-b^2+a^2+b^2=2ab\)
c)\(a\left(b+c\right)-b\left(c-a\right)+c\left(b-a\right)\)
\(=ab+ac+ab-bc+bc-ac\)
\(=ab+ab=2ab\)
d)\(\left(a+b\right)\left(c+d\right)-\left(a-b\right)\left(c-d\right)\)
\(=ac+ad+bc+bd-ac+ad+bc-bd\)
\(=2ad+2bc=2\left(ad+bc\right)\)