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Mathematics
Mathematics
Problem
Explain why
(
a
+
2
b
)
⋅
(
a
−
2
b
)
(\mathbf{a}+2\mathbf{b})\cdot(\mathbf{a}-2\mathbf{b})
(
a
+
2
b
)
⋅
(
a
−
2
b
)
simplifies to
∣
a
∣
2
−
4
∣
b
∣
2
|\mathbf{a}|^{2}-4|\mathbf{b}|^{2}
∣
a
∣
2
−
4∣
b
∣
2
when
a
⋅
b
=
0
\mathbf{a}\cdot\mathbf{b}=0
a
⋅
b
=
0
.
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