Tomas learned that the product of the polynomials (a + b)(a2 – ab + b2) was a special pattern that would result in a sum of cubes, a3 + b3. 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.

Accepted Solution

[tex]c. \: (2x + y)(4 {x}^{2} - 2xy + {y}^{2} )[/tex] ✅[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\orange{:}}}}}[/tex][tex](a + b)( {a}^{2} - ab + {b}^{2} )[/tex]Substituting the values of "a = 2x" and ''b = y" in the expression, we have [tex](2x + y)[( 2{x})^{2} - 2xy + {y}^{2} ] \\ = (2x + y)(4 {x}^{2} - 2xy + {y}^{2} )[/tex][tex]\large\mathfrak{{\pmb{\underline{\orange{Happy\:learning }}{\orange{.}}}}}[/tex]