Answer:
1) The polynomial [tex]8x^3+1[/tex] represents a sum of cubes
2) The polynomial [tex]49x^2-25[/tex] represents a difference of squares
Step-by-step explanation:
1) To find the polynomials represents a sum of cubes :
[tex]8x^3+1[/tex] represents a sum of cubes
For [tex]8x^3+1[/tex]
[tex]=2^3x^3+1^3[/tex]
[tex]=(2x)^3+1^3[/tex]
Therefore [tex]8x^3+1=(2x)^3+1^3[/tex]
Therefore [tex]8x^3+1[/tex] represents a sum of cubes
2)To find the polynomials represents a difference of squares :
[tex]49x^2-25[/tex] represents a difference of squares
For [tex]49x^2-25[/tex]
[tex]=7^2x^2-5^2[/tex]
[tex]=(7x)^2-5^2[/tex]
Therefore [tex]49x^2-25=(7x)^2-5^2[/tex]
Therefore [tex]49x^2-25[/tex] represents a difference of squares
