Jasonbradley
Home

(a+b+c)(a+b-c)

3 min read Jun 16, 2024
(a+b+c)(a+b-c)

Expanding (a + b + c)(a + b - c)

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

Using the Distributive Property:

  1. Treat (a + b + c) as a single term and distribute it to the second binomial: (a + b + c)(a + b - c) = (a + b + c) * a + (a + b + c) * b + (a + b + c) * (-c)

  2. Distribute again within each of the resulting terms: = a² + ab + ac + ab + b² + bc - ac - bc - c²

  3. Combine like terms: = a² + 2ab + b² - c²

Using the FOIL Method:

The FOIL method is a mnemonic acronym for First, Outer, Inner, Last. It helps us remember which terms to multiply together.

  1. Multiply the First terms: a * a = a²

  2. Multiply the Outer terms: a * (-c) = -ac

  3. Multiply the Inner terms: b * a = ab

  4. Multiply the Last terms: b * (-c) = -bc

  5. Multiply the First term of the first binomial by the remaining terms in the second binomial: (a + b + c) * b = ab + b² + bc

  6. Multiply the second term of the first binomial by the remaining terms in the second binomial: (a + b + c) * (-c) = -ac - bc - c²

  7. Combine all the terms: = a² - ac + ab - bc + ab + b² + bc - ac - c²

  8. Combine like terms: = a² + 2ab + b² - c²

Therefore, the expanded form of (a + b + c)(a + b - c) is a² + 2ab + b² - c².

Important Note: This expression can also be factored as a difference of squares: (a + b + c)(a + b - c) = [(a + b) + c][(a + b) - c] = (a + b)² - c². This can be helpful in solving equations or simplifying expressions.

Related Post

Featured Posts