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a^{2}-b^{2}-b\left(a-b\right)
Consider \left(a+b\right)\left(a-b\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.
a^{2}-b^{2}-\left(ba-b^{2}\right)
Use the distributive property to multiply b by a-b.
a^{2}-b^{2}-ba-\left(-b^{2}\right)
To find the opposite of ba-b^{2}, find the opposite of each term.
a^{2}-b^{2}-ba+b^{2}
The opposite of -b^{2} is b^{2}.
a^{2}-ba
Combine -b^{2} and b^{2} to get 0.
a^{2}-b^{2}-b\left(a-b\right)
Consider \left(a+b\right)\left(a-b\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.
a^{2}-b^{2}-\left(ba-b^{2}\right)
Use the distributive property to multiply b by a-b.
a^{2}-b^{2}-ba-\left(-b^{2}\right)
To find the opposite of ba-b^{2}, find the opposite of each term.
a^{2}-b^{2}-ba+b^{2}
The opposite of -b^{2} is b^{2}.
a^{2}-ba
Combine -b^{2} and b^{2} to get 0.