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(x-7)(x+4)

2 min read Jun 17, 2024
(x-7)(x+4)

Expanding the Expression (x-7)(x+4)

This article will explore the expansion of the expression (x-7)(x+4), using the distributive property or the FOIL method.

Expanding using the Distributive Property

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

  1. Treat (x-7) as a single term:

    (x-7)(x+4) = (x-7) * x + (x-7) * 4

  2. Distribute:

    (x-7) * x + (x-7) * 4 = x² - 7x + 4x - 28

  3. Combine like terms:

    x² - 7x + 4x - 28 = x² - 3x - 28

Expanding using the FOIL Method

FOIL is an acronym that stands for First, Outer, Inner, Last. It helps us remember the steps involved in multiplying two binomials:

  1. Multiply the First terms: x * x = x²

  2. Multiply the Outer terms: x * 4 = 4x

  3. Multiply the Inner terms: -7 * x = -7x

  4. Multiply the Last terms: -7 * 4 = -28

  5. Combine like terms: x² + 4x - 7x - 28 = x² - 3x - 28

Conclusion

Both methods, the distributive property and FOIL, lead to the same result: x² - 3x - 28. The choice of method is a matter of personal preference. The key is to understand how to apply the distributive property and to be able to combine like terms.

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