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Tomas learned that the product of the polynomials [tex](a+b)(a^2-ab+b^2)[/tex] was a special pattern that would result in a sum of cubes, [tex]a^3+b^3[/tex].
His teacher put four products on the board and asked the class to identify which product would result in a sum of cubes if [tex]a=2x[/tex] and [tex]b=y[/tex].

Sagot :

We are provided , Tomas learned that a³ + b³ = (a + b ) ( a² - ab + b² ) , 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) (4x²-2xy+y²) would result in the sum of cubes of 2x & y :D

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