Answer:
(4x² + 3)(16 - 12x² + 9)
Step-by-step explanation:
A sum of cubes factors as
a³ + b³ = (a + b)(a² - ab + b²)
64 = (4x²)³ ⇒ a = 4x²
27 = 3³ ⇒ b = 3
Hence
64 + 27
(4x² + 3)((4x²)² - (4x² × 3) + 3²)
= (4x² + 3)(16 - 12x² + 9)
The difference would be 74.059
The factors of 48 are:
1 x 48
2 x 24
3 x 16
4 x 12
6 x 8
and visa versa: 48 x 1 etc.
To make the product negative, one of the factors has to be positive and one has to be negative. To find the greatest sum, make the bigger number the positive factor and the smaller number the negative factor. So, -1 x 48 = -48 and the sum of -1 + 48 = 47 which would be the greatest possible sum.