Question

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

Answer 1

\(-(-a+c-d)-(c-a+d)\)

\(=a-c+d-c+a-d\)

\(=(a+a)-(c+c)+(d-d)\)

\(=2a-2c\)

\(-(a+b-c+d)+(a-b-c-d)\)

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

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

\(=0-0+2c-2d\)

\(=2c-2d\)

\(a(b-c-d)-a(b+c-d)\)

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

\(=a.0=0\)

\((a+b)(c+d)-(a+d)(b+c)\)

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

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

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

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

\((a+b)(c-d)-(a-b)(c+d)\)

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

\(=ac-ad+bc-bd-ac-ad+bc-bd\)

\(=(ac-ac)-(ad+ad)+(bc+bc)-(bd+bd)\)

\(=2ad+2bc-2bd\)

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

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

\(=2ab+2ab=4ab\)