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

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Solution

Area of rectangle = Length $\times$ Breadth

Then,

$A r e a = (x^{2} - x + 2) * (x^{2} + x - 2) = x^{2} (x^{2} + x - 2) - x (x^{2} + x - 2) + 2 (x^{2} + x - 2)$

$A r e a = (x^{4} + x^{3} - 2 x^{2}) + (- x^{3} - x^{2} + 2 x) + (2 x^{2} + 2 x - 4)$

$A r e a = x^{4} - x^{2} + 4 x - 4$

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