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2010-02-12T17:54:42+01:00

a) 2[(m-n)²-(m+n)²]-4(m-n)² =2[m²-2mn+n²-m²-2mn-n²]-4(m²-2mn+n²)=2(-4mn)-4m²+8mn-4n²=-8mn-4m²+8mn-4n²=-4(m²+n²)

b) ½[(a-2b)²-(2a+b)²-(a²-b²)] =1/2[a²-4ab+4b²-4a²-4ab-b²-a²+b²]=1/2[4a²-8ab+4b²]=2a²-4ab+2b²=2(a²-2ab+b²)=2(a+b)²
2010-02-12T18:04:36+01:00
A) =2[m²-2mn+n²-(m²+2mn+n²)]-4(m²-2mn+n²)=
=2(m²-2mn+n²-m²-2mn-n²)-4m²+8mn-4n²=
=2m²-4mn+2n²-2m²+4mn-2n²-4m²+8mn-4n²=-4m²-4n²+8mn

b) =½[a²-4ab+4b²-(4a²+4ab+b²)-(a⁴-2a²b²+b⁴)]=
=½(a²-4ab+4b²-4a²-4ab-b²-a⁴+2a²b²-b⁴)=
=½(-a⁴-3a²-b⁴+3b²+2a²b²-8ab)=
=-½a⁴-1½a²-½b⁴+1½b²+a²b²-4ab