Given posible expression for the length and breadth of rectangle whose area is 25x2 30xy+9y2-4z2
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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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