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Polynomial Arithmetic

From profit/cost models to the flight of a baseball to approximating the motion of a wave, polynomials are a mathematical way to represent values which are sums of powers of variables.

Level 2

         

\[\large \frac{ 11^4 - 9 ^ 4 } { 11 ^2 + 9^ 2 } = \ ? \]

\[ \large \left( \sqrt{{\color{red}60}} + {\color{blue}3}\sqrt{{\color{blue}7}}\right)^2\left( \sqrt{{\color{red}60}} - {\color{blue}3}\sqrt{{\color{blue}7}}\right)^2 = \ ?\]

\[ \large x+\frac{1}{x} = 5, \quad\quad\quad x^2 + \frac{1}{x^2} = \ ? \]

\[\large 10^x=(10^{624}+25)^2-(10^{624}-25)^2\]

What is the value of \(x\) that satisfies the equation above?

Which of the following equals \(\dfrac { { a }^{ 2 }-{ b }^{ 2 } }{ a-b } \) for \(a\neq b\)?

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