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\(=a^2\left(1-b^2\right)+b\left(b-1\right)+a\left(b-1\right)..\)
\(=a^2\left(1-b\right)\left(1+b\right)-b\left(1-b\right)-a\left(1-b\right).\)
\(=\left(a^2+a^2b-b-a\right)\left(1-b\right)\)
\(=\left(ab+a+b\right)\left(a-1\right)\left(1-b\right)\)
\(a^2+b^2-a^2b^2+ab-a-b\)
\(=a^2\left(1-b^2\right)+b\left(b-1\right)+a\left(b-1\right)\)
\(=a^2\left(1-b\right)\left(1+b\right)-b\left(1-b\right)-a\left(1-b\right)\)
\(=\left(a^2+a^2b-b-a\right)\left(1-b\right)\)
\(=\left(ab+a+b\right)\left(a-1\right)\left(1-b\right)\)
TL:
\(ab\left(a^2+b^2\right)-xy\left(a^2+b^2\right)\)
\(=\left(ab-xy\right)\left(a^2+b^2\right)\)
(ab-1)2 + (a+b)2
=a2b2-2ab+1+a2+2ab+b2
=a2b2+a2+b2+1
=a2(b2+1)+(b2+1)
=(a2+1)(b2+1)
\(a^3b-ab^3+a^2+2ab+b^2\)
\(=\left(a^3b-ab^3\right)+\left(a^2+2ab+b^2\right)\)
\(=ab\left(a^2-b^2\right)+\left(a+b\right)^2\)
\(=ab\left(a-b\right)\left(a+b\right)+\left(a+b\right)^2\)
\(=\left(a+b\right)\left[ab\left(a-b\right)+\left(a+b\right)\right]\)
\(=\left(a+b\right)\left(a^2b-ab^2+a+b\right)\)
ab-b2-a+b=(ab-b2)-(a-b)=b.(a-b)-(a-b)=(a-b).(b-1)