User:Twentysand

A common mistake when learning about exponents:
$(a^{2}+b^{2})^{3}\neq a^{6}+b^{6}$

To see why, lets expand the outer exponent:
$(a^{2}+b^{2})^{3}=(a^{2}+b^{2})\times (a^{2}+b^{2})\times (a^{2}+b^{2})$

Actually lets do this - since we know we can use the FOIL method to Distribute a square of sums:
$(a^{2}+b^{2})^{3}=(a^{2}+b^{2})^{2}\times (a^{2}+b^{2})$

We can now FOIL the first part:
$(a^{2}+b^{2})^{2}=a^{4}+(a^{2})(b^{2})+(a^{2})(b^{2})+b^{4}$

So now we have Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "http://localhost:6011/en.wikipedia.org/v1/":): {\displaystyle (a^2 + b^2)^3 = (a^4 + (a^2)(b^2) + (a^2)(b^2) + b^4) \times (a^2 + b^2) \, }

So we are left with a product of 2 expressions, we use a method that is similar to FOIL, but its not exactly the same since there are 4 terms in the first product. What we do is take the products of each combination of terms in the first expression and add them all together.
$=(a^{6}+2a^{4}b^{2}+a^{2}b^{4}+a^{4}b^{2}+2a^{2}b^{4}+b^{6})\,$