(x%5E2-x%2B1)-(x%5E3-9).jpeg "(x+1)(x^2-x+1)-(x^3-9)")
Simplifying the Expression (x+1)(x^2-x+1)-(x^3-9)
This article will guide you through the process of simplifying the algebraic expression (x+1)(x^2-x+1)-(x^3-9). We will use the distributive property and combine like terms to achieve a simplified form.
Step 1: Expand the First Product
The first part of the expression involves multiplying two binomials: (x+1) and (x^2-x+1). We can expand this using the distributive property:
(x+1)(x^2-x+1) = x(x^2-x+1) + 1(x^2-x+1)
Expanding further:
= x^3 - x^2 + x + x^2 - x + 1
Step 2: Combine Like Terms
Notice that some terms cancel out in the expanded expression:
= x^3 + 1
Step 3: Subtract the Second Term
Now, we subtract the second term, (x^3 - 9):
(x^3 + 1) - (x^3 - 9)
To subtract the second term, we distribute the negative sign:
= x^3 + 1 - x^3 + 9
Step 4: Combine Like Terms Again
Finally, we combine like terms:
= (x^3 - x^3) + (1 + 9)
= 10
Conclusion
Therefore, the simplified form of the expression (x+1)(x^2-x+1)-(x^3-9) is 10. This demonstrates that although the expression looks complex, through the application of algebraic principles, it can be simplified to a constant value.