madybrown2006
Answered

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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)

Sagot :

[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]

abidemiokin

The product that Tomas should choose should be (2x +y)(4x^2 – 2xy + y^2)

Sum of the cube of values

Given the sum of cubes expressd as:

a^3 + b^3 = (a + b)(a^2 – ab + b^2)

Given the following parametrs

a  = 2x

b = y

Substitute this values into the formula

a^3 + b^3 = (2x + y)((2x)^2 – 2xy + y^2)

a^3 + b^3 = (2x +y)(4x^2 – 2xy + y^2)

Hence the product that Tomas should choose should be (2x +y)(4x^2 – 2xy + y^2)

Learn more on sum of cubes here: https://brainly.com/question/26726803

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