Subjective Type

If two adjacent sides of a rectangle are $$5x^2 + 25xy + 4y^2$$ and $$2x^2 - 2xy + 3y^2$$, find its area.

Solution

Given,
The adjacent sides of a rectangle are $$5x^2 + 25xy + 4y^2$$ and $$2x^2 - 2xy +3y^2$$
So,
Area of rectangle = Product of two adjacent sides
= $$(5x^2 + 25xy + 4y^2) (2x^2 - 2xy + 3y^2)$$
= $$10x^4 - 10x^3y + 15x^2y^2 + 50x^3y - 50x^2y^2 + 75xy^3 + 8x^2y^2 - 8xy^3 + 12y^4$$
= $$10x^4 + 40x^3y - 27x^2y^2 + 67xy^3 + 12y^4$$
Thus,
The area of the rectangle is $$10x^4 + 40x^3y - 27x^2y^2 + 67xy^3 + 12y^4$$.

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