How Can You Quickly Simplify (x+a)^2 * (x-a)^2 to (x^2-a^2)^2?

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SUMMARY

The discussion focuses on simplifying the expression (x+a)^2 * (x-a)^2 to (x^2-a^2)^2 using algebraic identities. The key insight provided is to recognize that (x+a)^2 * (x-a)^2 can be viewed as ((x+a)(x-a))^2, which directly leads to (x^2-a^2)^2. This simplification leverages the identity A^2 * B^2 = (AB)^2, applying it effectively to the given expression.

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leolaw
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Which is the fastest way to simplify:
[tex](x+a)^2*(x-a)^2[/tex] to [tex](x^2-a^2)^2[/tex] ?
thx
 
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Think of [tex](x+a)^2*(x-a)^2[/tex] as [tex](x+a)*(x-a)*(x+a)*(x-a)[/tex] and [tex](x^2-a^2)[/tex] as [tex](x-a)*(x+a)[/tex]
 
There's the fastest way
[tex]A^{2}\cdot B^{2}=(AB)^{2}[/tex]

Apply it for your case.

Daniel.
 

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