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

Jasonbradley

2 min read

·

Jun 16, 2024

20

Share

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

This expression is a product of two binomials, and we can solve it using the distributive property or by recognizing a pattern.

Using the Distributive Property

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

1. Expand the first binomial: (a + b + c)(a + b - c) = a(a + b - c) + b(a + b - c) + c(a + b - c)

2. Distribute: = a² + ab - ac + ab + b² - bc + ac + bc - c²

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

Recognizing a Pattern

The expression (a + b + c)(a + b - c) resembles the difference of squares pattern: (x + y)(x - y) = x² - y².

In our case, we can consider (a + b) as 'x' and 'c' as 'y'.

Therefore:

(a + b + c)(a + b - c) = (a + b)² - c²

This can be further expanded as:

= a² + 2ab + b² - c²

Conclusion

Both methods lead to the same answer: a² + 2ab + b² - c².

This expression represents the simplified form of the product (a + b + c)(a + b - c).