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From Wikiversity
a
2
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b
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{\displaystyle a^{2}-b^{2}=(a+b)(a-b)}
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=
a
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a
2
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{\displaystyle (a+b)(a-b)=a^{2}+ab-ab+b^{2}=a^{2}-b^{2}}
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b
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2
=
a
2
+
2
a
b
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b
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{\displaystyle (a+b)^{2}=a^{2}+2ab+b^{2}}
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2
=
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(
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=
a
2
+
a
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a
b
+
b
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a
2
+
2
a
b
+
b
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{\displaystyle (a+b)^{2}=(a+b)(a+b)=a^{2}+ab+ab+b^{2}=a^{2}+2ab+b^{2}}
(
a
−
b
)
2
=
a
2
−
2
a
b
+
b
2
{\displaystyle (a-b)^{2}=a^{2}-2ab+b^{2}}
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a
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)
2
=
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a
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a
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{\displaystyle (a-b)^{2}=(a-b)(a-b)=a^{2}-ab-ab+b^{2}=a^{2}-2ab+b^{2}}
a
2
+
b
2
=
(
a
2
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{\displaystyle a^{2}+b^{2}=(a^{2}-b^{2})+2ab=(a^{2}+b^{2})-2ab}
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