The expression matches the identity form of a cube + b cube + c cube – 3abc where a = x, b = y and c = 4. Since the sum a + b + c equals 0, the entire ...
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We divide the given quadratic area expression by the given width binomial. Factoring the numerator 2x square + 7x + 3 yields (2x + 1)(x + 3) and cancelling the common width factor leaves the length.
The total outer side length including the path becomes 40 + 2s metres. Subtracting the inner square area (1600) from the expanded outer square area provides the final algebraic expression for the path.
We apply the difference of squares identity, x square – y square = (x + y)(x – y). Rewriting 36s square as (6s) square and 49t square as (7t) square directly provides the two unique linear dimensions.
This matches the three-term identity where the term containing variable b must be negative because both cross-product terms that include b have a minus sign in the expression.