tomas learned that the product of the polynomials (a + b)(a² - ab + b²) was a special pattern that would…

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. which product should tomas choose? (2x + y)(2x² + 2xy - y²) (2x + y)(4x² + 2xy - y²) (2x + y)(4x² - 2xy + y²) (2x + y)(2x² - 2xy + y²)

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. which product should tomas choose? (2x + y)(2x² + 2xy - y²) (2x + y)(4x² + 2xy - y²) (2x + y)(4x² - 2xy + y²) (2x + y)(2x² - 2xy + y²)

Answer

Explanation:

Step1: Recall sum - of - cubes formula

The sum - of - cubes formula is $(a + b)(a^{2}-ab + b^{2})=a^{3}+b^{3}$.

Step2: Substitute $a = 2x$ and $b = y$

When $a = 2x$ and $b = y$, we substitute these values into the left - hand side of the sum - of - cubes formula. We get $(2x + y)[(2x)^{2}-(2x)y + y^{2}]=(2x + y)(4x^{2}-2xy + y^{2})$.

Answer:

$(2x + y)(4x^{2}-2xy + y^{2})$