Question

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?

A) (2x + y)(2x2 + 2xy – y2)
B) (2x + y)(4x2 + 2xy – y2)
C) (2x + y)(4x2 – 2xy + y2)
D) (2x + y)(2x2 – 2xy + y2)

Answer 1

Answer:

C

Step-by-step explanation:

Tomas learned that

$a^3+b^3=(a+b)(a^2-ab+b^2)$

If $a=2x,\ b=y$, then

$a^3+b^3\\ \\=(2x)^3+y^3\\ \\=((2x)+y)((2x)^2-(2x)y+y^2)\\ \\=(2x+y)(4x^2-2xy+y^2)$

Answer 2

The product that Tomas should choose is $(2x+y)(4x^2-2xy+y^2)$

How to find the difference of cubes

Given the expression

$a^3+b^3=(a+b)(a^2-ab+b^2)$

Given the following parameters

a = 2x

b = y

Substitute into the expression to have:

$(2x)^3+y^3=(2x+y)((2x)^2-2xy+y^2)$

$(2x)^3+y^3=(2x+y)(4x^2-2xy+y^2)$

Hence the product that Tomas should choose is $(2x+y)(4x^2-2xy+y^2)$

Learn more on difference of cubes here: https://brainly.com/question/2747971