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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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