Question

Which polynomial represents a sum of cubes?

x^3+9

4x^3+1

8x^3+1

64x^3-27


Which of the following polynomials represents a difference of squares?


4x^2-8

9x^2+16

16x^2-2

49x^2-25

Answer 1

1) The polynomial
`8x^3+1` represents a sum of cubes

2) The polynomial
`49x^2-25` represents a difference of squares

Explanation:

1) To find the polynomials represents a sum of cubes :

`8x^3+1` represents a sum of cubes

For
`8x^3+1`

`=2^3x^3+1^3`

`=(2x)^3+1^3`

Therefore
`8x^3+1=(2x)^3+1^3`

Therefore
`8x^3+1` represents a sum of cubes

2)To find the polynomials represents a difference of squares :

`49x^2-25` represents a difference of squares

For
`49x^2-25`

`=7^2x^2-5^2`

`=(7x)^2-5^2`

Therefore
`49x^2-25=(7x)^2-5^2`

Therefore
`49x^2-25` represents a difference of squares