Evaluate
\left(1-a\right)\left(a+3\right)
Expand
3-2a-a^{2}
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4-\left(a^{2}+2a+1\right)
Use binomial theorem \left(p+q\right)^{2}=p^{2}+2pq+q^{2} to expand \left(a+1\right)^{2}.
4-a^{2}-2a-1
To find the opposite of a^{2}+2a+1, find the opposite of each term.
3-a^{2}-2a
Subtract 1 from 4 to get 3.
4-\left(a^{2}+2a+1\right)
Use binomial theorem \left(p+q\right)^{2}=p^{2}+2pq+q^{2} to expand \left(a+1\right)^{2}.
4-a^{2}-2a-1
To find the opposite of a^{2}+2a+1, find the opposite of each term.
3-a^{2}-2a
Subtract 1 from 4 to get 3.
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Limits
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