(x-8)(x+1)

2 min read Jun 17, 2024
(x-8)(x+1)

Understanding (x-8)(x+1)

This expression represents a product of two binomials, (x-8) and (x+1). To understand it fully, we need to explore its components and how they interact.

Binomials

Binomials are algebraic expressions with two terms. In our case:

  • (x-8): This binomial contains the variable 'x' and a constant term '-8'.
  • (x+1): This binomial also contains the variable 'x' and a constant term '+1'.

Expanding the Expression

To expand the expression, we use the distributive property. This means we multiply each term in the first binomial by each term in the second binomial:

  1. x * x = x²
  2. x * 1 = x
  3. -8 * x = -8x
  4. -8 * 1 = -8

Combining these results, we get:

(x-8)(x+1) = x² + x - 8x - 8

Simplifying the Expression

Finally, we combine like terms to simplify the expanded expression:

(x-8)(x+1) = x² - 7x - 8

Conclusion

Therefore, the expression (x-8)(x+1) represents a quadratic expression, x² - 7x - 8, after being expanded and simplified. This simplified form can be useful for solving equations, analyzing graphs, or other algebraic operations.

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