![\rm \: = \:[ \vec{A}.\vec{A} + \vec{A}.\vec{B} + \vec{B}.\vec{A} + \vec{B}.\vec{B}] - [\vec{A}.\vec{A} - \vec{A}.\vec{B} - \vec{B}.\vec{A} + \vec{B}.\vec{B}]](/tpl/images/2490/1616/eb014.png)
![\rm \: = \: [ { |\vec{A}| }^{2} + \vec{A}.\vec{B} + \vec{A}.\vec{B} + { |\vec{B}| }^{2}] - [ { |\vec{A}| }^{2} - \vec{A}.\vec{B} - \vec{A}.\vec{B} + { |\vec{B}| }^{2}]](/tpl/images/2490/1616/e799d.png)
![\rm \: = \: [ { |\vec{A}| }^{2} + 2\vec{A}.\vec{B} + { |\vec{B}| }^{2}] - [ { |\vec{A}| }^{2} -2 \vec{A}.\vec{B} + { |\vec{B}| }^{2}]](/tpl/images/2490/1616/ae602.png)
Show that: |A⃗ + B⃗ |² - |A⃗ - B⃗ |² = 4 A⃗.B⃗ .
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