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(x + a)(x +b)= x^2 + x(a+ b) + ab

If the adjace...

Question

If the adjacent sides of a rectangle are $(x^{2} - x + 2)$ units and $(x^{2} + x - 2)$ units long, find the area of the rectangle.

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Solution

We know that
area of a rectangle = length x breadth
Hence, area $= (x^{2} - x + 2) \times (x^{2} + x - 2)$
$= x^{4} + x^{3} - 2 x^{2} - x^{3} - x^{2} + 2 x + 2 x^{2} + 2 x - 4$
$= x^{4} - x^{2} + 4 x - 4$ square units.

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