Evaluate
a\left(a-3b\right)+a^{2}-b^{2}
Expand
2a^{2}-3ab-b^{2}
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a^{2}-b^{2}+a\left(a-3b\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}+a^{2}-3ab
Use the distributive property to multiply a by a-3b.
2a^{2}-b^{2}-3ab
Combine a^{2} and a^{2} to get 2a^{2}.
a^{2}-b^{2}+a\left(a-3b\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}+a^{2}-3ab
Use the distributive property to multiply a by a-3b.
2a^{2}-b^{2}-3ab
Combine a^{2} and a^{2} to get 2a^{2}.
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