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(2a+b-5)(2a-b+5)

2 min read Jun 16, 2024
(2a+b-5)(2a-b+5)

Expanding the Expression (2a + b - 5)(2a - b + 5)

This expression represents the product of two binomials. To expand it, we can use the FOIL method or distributive property.

Using FOIL Method

FOIL stands for First, Outer, Inner, Last. This method helps us systematically multiply each term of the first binomial by each term of the second binomial.

  1. First: Multiply the first terms of each binomial: (2a) * (2a) = 4a²
  2. Outer: Multiply the outer terms of each binomial: (2a) * (-b) = -2ab
  3. Inner: Multiply the inner terms of each binomial: (b) * (2a) = 2ab
  4. Last: Multiply the last terms of each binomial: (b) * (-b) = -b²
  5. Last: Multiply the last terms of each binomial: (-5) * (5) = -25

Now, we add all the resulting terms together: 4a² - 2ab + 2ab - b² - 25

Finally, combine like terms:

4a² - b² - 25

Using Distributive Property

We can also expand the expression using the distributive property. This involves distributing each term of the first binomial to each term of the second binomial.

  1. Distribute (2a): (2a)(2a) + (2a)(-b) + (2a)(5) = 4a² - 2ab + 10a
  2. Distribute (b): (b)(2a) + (b)(-b) + (b)(5) = 2ab - b² + 5b
  3. Distribute (-5): (-5)(2a) + (-5)(-b) + (-5)(5) = -10a + 5b - 25

Finally, add all the resulting terms together:

4a² - 2ab + 10a + 2ab - b² + 5b - 10a + 5b - 25

Combine like terms:

4a² - b² - 25

Therefore, the expanded form of (2a + b - 5)(2a - b + 5) is 4a² - b² - 25.

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