Question

Give possible expressions for the length and breadth of rectangle whose area is 25x square +30xy+9ysquare-4zsquare

Answer 1

5x + 3y + 2z   & 5x + 3y - 2z are possible expressions for the length and breadth of rectangle with Area 25x² + 30xy +9y² – 4z²

Step-by-step explanation:

Area of Rectangle = 25x² + 30xy +9y² – 4z²

= (5x)² + 2(5x)(3y) + (3y)² - (2z)²

using a² + 2ab + b² = (a + b)²

a = 5x  & b = 3y

= (5x + 3y)² - (2z)²

Now using a² - b² = (a + b)(a - b)

a = 5x + 3y & b = 2z

= (5x + 3y + 2z)(5x + 3y - 2z)

Area of Rectangle  = (5x + 3y + 2z)(5x + 3y - 2z)

possible expressions for the length and breadth of rectangle

=  5x + 3y + 2z   & 5x + 3y - 2z

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