tomas learned that the product of the polynomials $(a + b)(a^{2}-ab + b^{2})$ was a special pattern that…

tomas learned that the product of the polynomials $(a + b)(a^{2}-ab + b^{2})$ 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 $b = y$. which product should tomas choose? $(2x + y)(2x^{2}+2xy - y^{2})$ $(2x + y)(4x^{2}+2xy - y^{2})$ $(2x + y)(4x^{2}-2xy + y^{2})$ $(2x + y)(2x^{2}-2xy + y^{2})$

tomas learned that the product of the polynomials $(a + b)(a^{2}-ab + b^{2})$ 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 $b = y$. which product should tomas choose? $(2x + y)(2x^{2}+2xy - y^{2})$ $(2x + y)(4x^{2}+2xy - y^{2})$ $(2x + y)(4x^{2}-2xy + y^{2})$ $(2x + y)(2x^{2}-2xy + y^{2})$

Answer

Explanation:

Step1: Substitute (a = 2x) and (b = y) into the formula ((a + b)(a^{2}-ab + b^{2}))

When (a = 2x), (a^{2}=(2x)^{2}=4x^{2}). When (a = 2x) and (b = y), (ab=(2x)\times y = 2xy), and (b^{2}=y^{2})

Step2: Write out the product

The product ((a + b)(a^{2}-ab + b^{2})) with (a = 2x) and (b = y) is ((2x + y)(4x^{2}-2xy + y^{2}))

Answer:

((2x + y)(4x^{2}-2xy + y^{2})) (the third option)