Step-by-step explanation:
length × breadth = x² + 5x - 36
let's find, what expression was multiplied by what expression to give that result.
first we see, we have a pure x² term.
so, both start with (x + ...) or (x - ...).
then we see the last (constant) term -36.
so, we have a
(x + a)(x - b)
situation.
36 is the product of
6×6
9×4
12×3
18×2
the term +5x tells us that the difference between a and b must be 5. and a as the positive number must be bigger to give us the "+" (the multiplication contains "... + ax - bx ...").
and that means a = +9, b = -4
so, the original area calculation was
(x + 9)(x - 4) = x² + 5x - 36
when we decrease both factors by 2, we get
(x + 9 - 2)(x - 4 - 2) = (x + 7)(x - 6) = x² + x - 42
that is the new area of the rectangle.
