Answer :
To determine what kind of expression the polynomial [tex]\(x^3 + 64\)[/tex] represents, let's analyze it:
1. Identify the form of the polynomial:
- The polynomial is [tex]\(x^3 + 64\)[/tex].
- Notice that 64 can be written as [tex]\(4^3\)[/tex].
2. Consider the sum of cubes:
- The expression [tex]\(x^3 + 64\)[/tex] can be rewritten as [tex]\(x^3 + 4^3\)[/tex].
- This matches the form of a sum of cubes, which is generally expressed as [tex]\(a^3 + b^3\)[/tex].
3. Recall the formula for the sum of cubes:
- The sum of cubes formula is [tex]\(a^3 + b^3 = (a + b)(a^2 - ab + b^2)\)[/tex].
4. Apply the sum of cubes formula:
- Here, [tex]\(a = x\)[/tex] and [tex]\(b = 4\)[/tex].
- The formula for this particular expression becomes:
[tex]\((x + 4)(x^2 - 4x + 16)\)[/tex].
Therefore, the polynomial [tex]\(x^3 + 64\)[/tex] is identified as a sum of cubes.
1. Identify the form of the polynomial:
- The polynomial is [tex]\(x^3 + 64\)[/tex].
- Notice that 64 can be written as [tex]\(4^3\)[/tex].
2. Consider the sum of cubes:
- The expression [tex]\(x^3 + 64\)[/tex] can be rewritten as [tex]\(x^3 + 4^3\)[/tex].
- This matches the form of a sum of cubes, which is generally expressed as [tex]\(a^3 + b^3\)[/tex].
3. Recall the formula for the sum of cubes:
- The sum of cubes formula is [tex]\(a^3 + b^3 = (a + b)(a^2 - ab + b^2)\)[/tex].
4. Apply the sum of cubes formula:
- Here, [tex]\(a = x\)[/tex] and [tex]\(b = 4\)[/tex].
- The formula for this particular expression becomes:
[tex]\((x + 4)(x^2 - 4x + 16)\)[/tex].
Therefore, the polynomial [tex]\(x^3 + 64\)[/tex] is identified as a sum of cubes.
