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.

(x^{4} - x^{2} + 4 x - 4)

square units

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(x^{4} - x^{3} - x^{2} - 4 x)

square units

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(x^{4} - 5 x^{3} - x^{2})

square units

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(x^{4} - x^{3} - 4 x^{2} + 4)

square units

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Solution

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

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Similar questions

The adjacent sides of a rectangle are $x^{2} - 4 x y + 7 y^{2} a n d x^{3} - 5 x y^{2}$ .Find its area.

(x^{2} - x + 2)

(x^{2} + x - 2)

(x^{2} - x + 2)

(x^{2} + x - 2)

(x^{2} - x - 2)

(x^{2} + x - 2)

x^{4} - x^{2} + 4 x - 4

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