Question
Download Solution PDFSimplify (5x − 2y)2 + (2x + 5y)2 + (5x + 2y)(5x − 2y).
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
Simplify (5x - 2y)2 + (2x + 5y)2 + (5x + 2y)(5x - 2y).
Formula used:
(a - b)2 = a2 - 2ab + b2
(a + b)2 = a2 + 2ab + b2
(a + b)(a - b) = a2 - b2
Calculation:
(5x - 2y)2 = 25x2 - 20xy + 4y2
(2x + 5y)2 = 4x2 + 20xy + 25y2
(5x + 2y)(5x - 2y) = 25x2 - 4y2
⇒ (5x - 2y)2 + (2x + 5y)2 + (5x + 2y)(5x - 2y)
⇒ (25x2 - 20xy + 4y2) + (4x2 + 20xy + 25y2) + (25x2 - 4y2)
⇒ 25x2 + 4x2 + 25x2 - 20xy + 20xy + 4y2 + 25y2 - 4y2
⇒ 54x2 + 25y2
∴ The correct answer is option (3).
Last updated on Jul 21, 2025
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