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.

Answer 1

The required product should be
`(2x)^3+(y)^3=(2x+y)(4x^2-2xy+y^2)`

Explanation:

Consider the provided information.

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`.

From the above information it is given that:

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

Substitute a = 2x and b = y in above and solve.

`(2x)^3+(y)^3=(2x+y)[(2x)^2-(2x)(y)+(y)^2]`

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

Hence, the required product should be
`(2x)^3+(y)^3=(2x+y)(4x^2-2xy+y^2)`

Answer 2

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

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)