Mathematics
Answer
75(x + y)2 - 48(x - y)2
= 3 x (25(x + y)2 - 16(x - y)2)
= 3 x [(5(x + y))2 - (4(x - y))2]
= 3 x [(5x + 5y)2 - (4x - 4y)2]
Using the formula
[∵ (x2 - y2) = (x + y)(x - y)]
= 3((5x + 5y) + (4x - 4y))((5x + y) - (4x - 4y))
= 3(5x + 5y + 4x - 4y)(5x + 5y - 4x + 4y)
= 3(5x + 4x + 5y - 4y)(5x - 4x + 5y + 4y)
= 3(9x + y)(x + 9y)
Hence,75(x + y)2 - 48(x - y)2 = 3(9x + y)(x + 9y)