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(2x-1)(x-5)

2 min read Jun 16, 2024
(2x-1)(x-5)

Expanding the Expression (2x-1)(x-5)

The expression (2x-1)(x-5) represents the product of two binomials. To simplify 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 given expression:

  1. Distribute (2x-1) over (x-5): (2x - 1)(x - 5) = 2x(x - 5) - 1(x - 5)

  2. Distribute again: 2x(x - 5) - 1(x - 5) = 2x² - 10x - x + 5

  3. Combine like terms: 2x² - 10x - x + 5 = 2x² - 11x + 5

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: 2x * x = 2x²

  2. Outer: Multiply the outer terms of each binomial: 2x * -5 = -10x

  3. Inner: Multiply the inner terms of each binomial: -1 * x = -x

  4. Last: Multiply the last terms of each binomial: -1 * -5 = 5

  5. Combine like terms: 2x² - 10x - x + 5 = 2x² - 11x + 5

Conclusion

Both methods lead to the same simplified expression: 2x² - 11x + 5. This expression is now in standard polynomial form, with the terms arranged in descending order of their exponents.

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