is the dot product of(a+b) . (a + b)= a^2 + b^2 + 2ab ?

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- Mar 10th 2009, 11:11 AMdopidot product verification
is the dot product of

**(a+b) . (a + b)**= a^2 + b^2 + 2ab ? - Mar 10th 2009, 01:26 PMProve It
- Mar 10th 2009, 01:48 PMPlato
That is more or less correct!

But it should be written as $\displaystyle \left( {a + b} \right) \cdot \left( {a + b} \right) = a \cdot a + 2a \cdot b + b \cdot b$.

**Please note that the ‘dot products’ in the answer**.

In fact here is an important form: $\displaystyle \left( {a + b} \right) \cdot \left( {a + b} \right) = \left\| a \right\|^2 + 2a \cdot b + \left\| b \right\|^2 $

**No that is not correct!**

To see where you went wrong, recall $\displaystyle v \cdot \left( {u + w} \right) = v \cdot u + v \cdot w$.

Let $\displaystyle v = \left( {a + b} \right)\;,\,u = a\;\& \,w = b$ and apply the distribution rule twice.