Question

Tomas learned that the product of the polynomials rmula1" title="(a+b)(a^2-ab+b^2)" alt="(a+b)(a^2-ab+b^2)" align="absmiddle" class="latex-formula"> was a special pattern that would result in a sum of cubes, $a^3+b^3$.
His teacher put four products on the board and asked the class to identify which product would result in a sum of cubes if $a=2x$ and $b=y$.

Answer 1

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 :

${:\implies \quad \sf (2x)^{3}+(y)^{3}=(2x+y)\{(2x)^{2}-2\cdot x\cdot y+(y)^{2}\}}$

${:\implies \quad \bf \therefore \quad \underline{\underline{(2x)^{3}+(y)^{3}=(2x+y)(4x^{2}-2xy+y^{2})}}}$

Hence , The product (2x+y) (4x²-2xy+y²) would result in the sum of cubes of 2x & y :D