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.

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

Step-by-step explanation:

a= 2x and b = y

then a^3 + b^3 = ?

We know that:

a^3+b^3 = (a + b)(a^2 – ab + b^2)

Putting a =2x and b=y and finding the answer

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

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

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

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