Question

Bài 8:Bỏ dấu ngoặc rồi rút gọn biểu thức

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

Answer 1

d, \(\left(a+b\right)\left(c+d\right)-\left(a+d\right)\left(b+c\right)\)

\(=ac+ad+bc+bd-ab-ac-db-dc\)

\(=ad+bc-ab-cd\)

\(=a\left(b-d\right)+c\left(b-d\right)\)

\(=\left(a+c\right)\left(b-d\right)\)

e, \(\left(a+b\right)\left(c-d\right)-\left(a-b\right)\left(c+d\right)\)

\(=\left(a+b\right)\left(c-d\right)-\left(a+b\right)\left(d-c\right)\)

\(=\left(a+b\right)\left(c-d-d+c\right)\)

\(=\left(a+b\right)\left(2c-2d\right)\)

\(=2\left(a+b\right)\left(c-d\right)\)

f, \(\left(a+b\right)^2-\left(a-b\right)^2\)

\(=\left(a+b-a+b\right)\left(a+b+a-b\right)\)

\(=2b.2a=4ab\)

Answer 2

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) \(\left(a+b\right)^2-\left(a-b\right)^2\)

\(=\left(a+b\right)\left(a+b\right)-\left(a-b\right)\left(a-b\right)\)

\(=a^2+2ab+b^2-a^2+2ab-b^2\)

\(=4ab\)