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

$x^{4} - 5 x^{3} - x^{2}$

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$x^{4} - x^{3} - 4 x^{2} + 4$

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$x^{4} - x^{3} - x^{2} - 4 x$

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

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Solution

The correct option is D
$x^{4} - x^{2} + 4 x - 4$

Area of the rectangle = $l e n g t h \times b r e a d t h$

$(x^{2} - x + 2) \times (x^{2} + x - 2)$
$= x^{4} + x^{3} - 2 x^{2} - x^{3} - x^{2} + 2 x + 2 x^{2} + 2 x - 4$
= $x^{4} - x^{2} + 4 x - 4$ sq cm

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Answer:

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If the length and breadth of a rectangle are (x2−x+2) cm and (x2+x−2) cm respectively, find the area of the rectangle.

The correct option is D x4−x2+4x−4 Area of the rectangle = length×breadth (x2−x+2)× (x2+x−2) =x4+x3−2x2−x3−x2+2x+2x2+2x−4 =x4−x2+4x−4 sq cm

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

The correct option is D
$x^{4} - x^{2} + 4 x - 4$

Area of the rectangle = $l e n g t h \times b r e a d t h$

$(x^{2} - x + 2) \times (x^{2} + x - 2)$
$= x^{4} + x^{3} - 2 x^{2} - x^{3} - x^{2} + 2 x + 2 x^{2} + 2 x - 4$
= $x^{4} - x^{2} + 4 x - 4$ sq cm