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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.

Using Difference of Two Squares

Given that $$x^2 - y^2 = (x-y) ( x+y)$$, what is the value of $$31 ^2 - 19 ^2$$?

Given that $$a^4 - b^4 = (a^2 - b^2)(a^2 + b^2) = (a-b)(a+b)(a^2 + b^2 )$$, what is the value of $$5 ^4 - 4 ^4$$?

If $$x+y=6$$, $$x-y=2$$ and $$x^2+y^2=20$$, what is the value of $x^4-y^4?$

Evaluate the above expression.

Find the positive value of $$N$$ such that $N^2 = 169.$

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