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Factoring

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u_{xx} - 3u_{xt} - 4u_{tt} = 0, How does this factor to:

(u_x + u_t)*(u_x-4u_t) = 0?

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Solution Summary

The solution provides an example of factoring an equation.

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First of all, let's look at (A - B)^2 = A^2 - 2AB + B^2
The central idea of completing the square is to try to arrange the polynomial to the form of A^2 - 2AB + B^2 by adding for subtracting terms. Let's simplify the expression first:

u_{xx} - 3u_{xt} - 4u_{tt} = 0

(u_x)(u_x) - 3(u_x)(u_t) - 4(u_t)(u_t) = 0

(u_x)^2 - 3(u_x)(u_t) - 4(u_t)^2 = 0

Now, let a = u_x and b = ...

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