Question

HI

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 1

SOLUTION

TO CHOOSE THE CORRECT OPTION

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)

EVALUATION

Here it is given that 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

$\sf {a}^{3} + {b}^{3} = (a + b)( {a}^{2} - ab + {b}^{2} )$

Now it is given that a = 2x and b = y.

Thus from above we get

$\sf {(2x)}^{3} + {(y)}^{3} = (2x+ y) \{{(2x)}^{2} - 2x.y + {(y)}^{2} \}$

$\sf \implies 8{x}^{3} + {y}^{3} = (2x+ y)(4 {x}^{2} - 2xy + {y}^{2} )$

FINAL ANSWER

Hence the correct option is

(2x + y)(4x² - 2xy + y²)

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Answer 2

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Step-by-step explanation:

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