Math Problem Statement

(1 - √3)(√3 + 1)

Solution

To solve the given expression:

(13)(3+1)(1 - \sqrt{3})(\sqrt{3} + 1)

we can use the distributive property (FOIL method), which states that:

(ab)(c+d)=ac+adbcbd(a - b)(c + d) = ac + ad - bc - bd

Applying this to the expression:

  1. 13=31 \cdot \sqrt{3} = \sqrt{3}
  2. 11=11 \cdot 1 = 1
  3. 33=3-\sqrt{3} \cdot \sqrt{3} = -3
  4. 31=3-\sqrt{3} \cdot 1 = -\sqrt{3}

Adding these results together gives:

3+133=13=2\sqrt{3} + 1 - 3 - \sqrt{3} = 1 - 3 = -2

So, the simplified result of the expression is:

2-2

Would you like more details or have any questions?

Related Questions:

  1. How does the distributive property work with expressions containing square roots?
  2. Can you explain how to simplify expressions with radicals further?
  3. What are the steps to solve more complex radical expressions?
  4. How does this process change if there are more terms in the expression?
  5. How can the result be verified using another method?

Tip:

When working with radicals, remember that aa=a\sqrt{a} \cdot \sqrt{a} = a, which can help simplify the expressions quickly.

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Algebra
Radicals
Distributive Property

Formulas

(a - b)(c + d) = ac + ad - bc - bd

Theorems

Distributive Property
Simplification of Radicals

Suitable Grade Level

Grades 8-10