Question

Which polynomial represents a sum of cubes?

Answer 1

Answer:

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

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

Step-by-step 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