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#mathematics #polynomials #precalculus
Since the two factors are different by \2b\, the factors will always have the same parity. That is, if \(a-b\) is even then \(a+b\) must also be even, so the product is divisible by four. Or neither are divisible by 2, so the product is odd. This implies that numbers which are multiple of 2 but not 4 cannot be expressed as the difference of 2 squares.
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Difference Of Squares | Brilliant Math & Science Wiki
lor{blue}{2014} \times \color{blue}{2014}\color{blue}{2014} - \color{blue}{2014}\color{red}{2013} \times \color{blue}{2014}\color{fuchsia}{2015} = ? \] Don't use a calculator! Further Extension <span>Since the two factors are different by \(2b\), the factors will always have the same parity. That is, if \(a-b\) is even then \(a+b\) must also be even, so the product is divisible by four. Or neither are divisible by 2, so the product is odd. This implies that numbers which are multiple of 2 but not 4 cannot be expressed as the difference of 2 squares. The product of two differences of two squares is itself a difference of two squares in two different ways: \[\begin{array} { l l l } \left(a^2-b^2\right)\left(c^2-d^2\right) &= (ac)


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