We are provided , Tomas learned that aΒ³ + bΒ³ = (a + b ) ( aΒ² - ab + bΒ² ) , and his teacher writes four products on the board and we have to tell that which product suits the best if a = 2x and b = y
Now , putting a = 2x , b = y in the given formula we have :
[tex]{:\implies \quad \sf (2x)^{3}+(y)^{3}=(2x+y)\{(2x)^{2}-2\cdot x\cdot y+(y)^{2}\}}[/tex]
[tex]{:\implies \quad \bf \therefore \quad \underline{\underline{(2x)^{3}+(y)^{3}=(2x+y)(4x^{2}-2xy+y^{2})}}}[/tex]
Hence , The product (2x+y) (4xΒ²-2xy+yΒ²) would result in the sum of cubes of 2x & y :D
