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(x+1)(x-4)

2 min read Jun 16, 2024
(x+1)(x-4)

Expanding (x+1)(x-4)

The expression (x+1)(x-4) is a product of two binomials. To expand this expression, we can use the distributive property or the FOIL method.

Using the Distributive Property

The distributive property states that a(b+c) = ab + ac. We can apply this property twice to expand the expression:

  1. Distribute (x+1) over (x-4): (x+1)(x-4) = x(x-4) + 1(x-4)

  2. Distribute x and 1: x(x-4) + 1(x-4) = x² - 4x + x - 4

  3. Combine like terms: x² - 4x + x - 4 = x² - 3x - 4

Using the FOIL Method

FOIL stands for First, Outer, Inner, Last. This method provides a systematic way to multiply binomials.

  1. First: Multiply the first terms of each binomial: x * x = x²

  2. Outer: Multiply the outer terms of the binomials: x * -4 = -4x

  3. Inner: Multiply the inner terms of the binomials: 1 * x = x

  4. Last: Multiply the last terms of each binomial: 1 * -4 = -4

  5. Combine like terms: x² - 4x + x - 4 = x² - 3x - 4

Conclusion

Both methods lead to the same result: (x+1)(x-4) = x² - 3x - 4. This expanded form represents a quadratic expression.

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