Sử dụng tính chất phân phối của phép nhân đối với phép cộng đưa các tích sau về dạng tổng:
1) (a+b).(a+b)
2) (a-b)2
3) (a+b).(a-b)
4) (a+b)3
5) (a-b)3
6) (a+b).(a2-ab+b2)
7) (a-b).(a2+ab+b2)
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Những câu hỏi liên quan
1 tháng 7 2016
Cái này lên lớp 8 mới hok nhưng bạn chịu khó hiểu nha :
\(\left(a+b\right)\left(a^2-ab+b^2\right)\)
\(=a^3-a^2b+ab^2+a^2b-ab^2+b^3\)
Ta thấy dấu - vs dấu + triệt tiêu nha còn :
\(=a^3+b^3\)
Thế là xong
Ủng hộ mik nha
Thnaks
21 tháng 5 2018
1) \(\left(a+b\right).\left(a+b\right)=a.\left(a+b\right)+b.\left(a+b\right)=a^2+ab+b^2+ab\)
2) \(\left(a-b\right)^2=\left(a-b\right).\left(a-b\right)=a.\left(a-b\right)-b.\left(a-b\right)=a^2-ab-ab+b^2\)
\(=a^2+\left(-ab\right)+\left(-ab\right)+b^2\)
3) \(\left(a+b\right).\left(a-b\right)=a.\left(a-b\right)+b.\left(a-b\right)=a^2-ab+ab-b^2=a^2-b^2\)
\(=a^2+-\left(b^2\right)\)
4) \(\left(a+b\right)^3=\left(a+b\right).\left(a+b\right).\left(a+b\right)=a.\left(a+b\right).\left(a+b\right)+b.\left(a+b\right).\left(a+b\right)\)
\(=\left[a.\left(a+b\right)\right].\left(a+b\right)+\left[b.\left(a+b\right)\right].\left(a+b\right)=\left(a^2+ab\right).\left(a+b\right)+\left(ab+b^2\right).\left(a+b\right)\)
\(=a^2.\left(a+b\right)+ab.\left(a+b\right)+ab.\left(a+b\right)+b^2.\left(a+b\right)\)
\(=a^3+a^2b+a^2b+ab^2+a^2b+ab^2+b^2a+b^3\)
5) \(\left(a-b\right)^3=\left(a-b\right).\left(a-b\right).\left(a-b\right)=a.\left(a-b\right).\left(a-b\right)-b.\left(a-b\right).\left(a-b\right)\)
\(=\left(a^2-ab\right).\left(a-b\right)-\left(ba-b^2\right).\left(a-b\right)\)
\(=a^2.\left(a-b\right)-ab.\left(a-b\right)-ba.\left(a-b\right)+b^2.\left(a-b\right)\)
\(=a^3-a^2b-a^2b+ab^2-ba^2+b^2a-ba^2+b^2a-b^3\)
6) \(\left(a+b\right).\left(a^2-ab+b^2\right)=a.\left(a^2-ab+b^2\right)+b.\left(a^2-ab+b^2\right)\)
\(=a^3-a^2b+ab^2+ba^2-ab^2+b^3\)
\(=a^3+b^3\)
7) \(\left(a-b\right).\left(a^2+ab+b^2\right)=a.\left(a^2+ab+b^2\right)-b.\left(a^2+ab+b^2\right)\)
\(=a^3+a^2b+ab^2-ba^2-ab^2-b^3\)
\(=a^3-b^3\)
HP
21 tháng 5 2018
1 a^2+2ab+b^2
2 a^2-2ab+b^2
3 a^2-b^2
4 a^3+3a^2b+3ab^2+b^3
5 a^3-3a^2b+3ab^2-b^3
6 a^3+b^3
7 a^3-b^3
K
4 tháng 7 2016
1) (a+b).(a+b)=a^2+ab+ba+b^2
=a^2+2ab+b^2
2)(a-b)^2=(a-b).(a-b)=a^2-ab-ab+b^2=a^2-2ab+b^2
3)(a+b).(a-b)=a^2-ab+ba-b^2=a^2-b^2
4 tháng 7 2016
Chữ Shin còn viết sai nữa à Tiểu Shyn?????????????????????????????????????????????????????????????????????????????\ ??????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????
K na
DD
18 tháng 8 2016
1) (a+b)3=(a+b)(a+b)(a+b)=(a2+ab+ab+b2)(a+b)=(a2+2ab+b2)(a+b)(a3+2a2b+ab2)+(a2b+2ab2+b3)=a3+2a2b+ab2+a2b+2ab2+b3
=a3+3a2b+3ab2+b3
21 tháng 5 2018
a) \(\left(a+b\right).\left(a-b\right)=a.\left(a-b\right)+b.\left(a-b\right)=a^2-ab+ba-b^2\)\(=a^2-b^2\)
b) \(\left(a+b\right)^3=\left(a+b\right).\left(a+b\right).\left(a+b\right)=a.\left(a+b\right).\left(a+b\right)+b.\left(a+b\right).\left(a+b\right)\)
\(=\left(a^2+ab\right).\left(a+b\right)+\left(ba+b^2\right).\left(a+b\right)\)\(=a^2.\left(a+b\right)+ab.\left(a+b\right)+ba.\left(a+b\right)+b^2.\left(a+b\right)\)
\(=a^3+a^2b+a^2b+ab^2+ba^2+b^2a+b^2a+b^3\)\(=a^3+3a^2b+3ab^2+b^3\)
c) \(\left(a+b\right).\left(a^2-ab+b^2\right)=a.\left(a^2-ab+b^2\right)+b.\left(a^2-ab+b^2\right)\)
\(=a^3-a^2b+ab^2+ba^2-ab^2+b^3\)\(=a^3+b^3\)
d) \(\left(a-b\right).\left(a^2+ab+b^2\right)=a.\left(a^2+ab+b^2\right)-b.\left(a^2+ab+b^2\right)\)
\(=a^3+a^2b+ab^2-ba^2-ab^2-b^3\)\(=a^3-b^3\)
e) \(\left(a-b\right)^3=\left(a-b\right).\left(a-b\right).\left(a-b\right)=a.\left(a-b\right).\left(a-b\right)-b.\left(a-b\right).\left(a-b\right)\)
\(=\left(a^2-ab\right).\left(a-b\right)-\left(ba-b^2\right).\left(a-b\right)\)\(=a^2.\left(a-b\right)-ab.\left(a-b\right)-ba.\left(a-b\right)+b^2.\left(a-b\right)\)
\(=a^3-a^2b-a^2b+ab^2-ba^2+b^2a+b^2a-b^3\)
\(=a^3-3a^2b+3ab^2-b^3\)
21 tháng 5 2018
1) (a+b).(a+b)=(a+b)2=a2+2ab+b2
2) (a-b)2=a2-2ab+b2
3) (a+b).(a-b)=a2-b2
4) (a+b)3=a3+3a2b+3ab2+b3
5) (a-b)3=a3-3a2b+3ab2-b3
6) (a+b).(a2-ab+b2)=a3+b3
7) (a-b).(a2+ab+b2)=a3-b3
1 tháng 6 2015
\(\left(a-b\right)^2=\left(a-b\right)\left(a-b\right)=\left(a-b\right).a-\left(a-b\right).b=a^2-ab-\left(ab-b^2\right)=a^2-ab-ab+b^2=a^2-2.ab+b^2\)
\(\left(a-b\right)^3=\left(a-b\right)^2.\left(a-b\right)=\left(a^2-2.ab+b^2\right).\left(a-b\right)=\left(a^2-2ab+b^2\right).a-\left(a^2-2ab+b^2\right).b\)\(=\left(a^3-2.a^2.b+a.b^2\right)-\left(b.a^2-2.b^2.a+b^3\right)=a^3-2.a^2.b+a.b^2-b.a^2+2.b^2.a-b^3=a^3-3.a^2.b+3.b^2.a-b^3\)
1) (a+b).(a+b)=(a+b)2=a2+2ab+b2
2) (a-b)2=a2-2ab+b2
3) (a+b).(a-b)=a2-b2
4) (a+b)3=a3+3a2b+3ab2+b3
5) (a-b)3=a3-3a2b+3ab2-b3
6) (a+b).(a2-ab+b2)=a3+b3
7) (a-b).(a2+ab+b2)=a3-b3
mấy cái ày là hằng đẳng thức đáng nhớ mà
lấy a+a b+b
lấy b^2-a
lấy a.b b.a
a^3 +b
b^3-a
hai câu cuối thì mình k biết