Question
$(a - b)^2+ \_\_\_\_\_\_\_\_\_\_\_\_ = a^2 - b^2$
✓
Answer
$(a - b)^2+ $ $2ab - 2b^2$ $= a^2- b^2$
Solution:
Let $(a-b)^2+x=a^2-b^2 $
$a^2+b^2-2 a b+x=a^2-b^2 $
$ x=a^2-b^2-\left(a^2+b^2-2 a b\right) $
$ =a^2-b^2-a^2-b^2+2 a b $
$ =2 a b-2 b^2 $
Solution:
Let $(a-b)^2+x=a^2-b^2 $
$a^2+b^2-2 a b+x=a^2-b^2 $
$ x=a^2-b^2-\left(a^2+b^2-2 a b\right) $
$ =a^2-b^2-a^2-b^2+2 a b $
$ =2 a b-2 b^2 $
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