1) m(m+n)+n(m+n)-9m²=(m+n)(m+n)-9m² = (m+n)²-3²m²=(m+n-3m)(m+n+3m)=(n-2m)(4m+n)
2) x(x-y)+y(y-x)-y²=(x-y)(x-y)-y²=(x-y)²-y²=(x-y-y)(x-y+y)=(x-2y)x
3) a(a+b+1)+b(a+b+1)+(a+b+1)-1=(a+b+1)(a+b+1)-1=(a+b+1)²-1=(a+b+1+1)(a+b+1-1)=(a+b+2)(a+b)
4) 16+2(m+n-2)-n(m+n-2)-m(m+n-2)=16+(m+n-2)(2-n-m)=4²-(m+n-2)²=(4-m-n+2)(4+m+n-2)=(6-m-n)(2+m+n)
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Answers & Comments
1) m(m+n)+n(m+n)-9m²=(m+n)(m+n)-9m² = (m+n)²-3²m²=(m+n-3m)(m+n+3m)=(n-2m)(4m+n)
2) x(x-y)+y(y-x)-y²=(x-y)(x-y)-y²=(x-y)²-y²=(x-y-y)(x-y+y)=(x-2y)x
3) a(a+b+1)+b(a+b+1)+(a+b+1)-1=(a+b+1)(a+b+1)-1=(a+b+1)²-1=(a+b+1+1)(a+b+1-1)=(a+b+2)(a+b)
4) 16+2(m+n-2)-n(m+n-2)-m(m+n-2)=16+(m+n-2)(2-n-m)=4²-(m+n-2)²=(4-m-n+2)(4+m+n-2)=(6-m-n)(2+m+n)