Math Problem Statement

2(10x2^n-1-6)

Solution

Let's simplify the given expression:

2(10x2n16)2(10x2^{n-1}-6)

Step 1: Distribute the 2 to each term inside the parentheses.

=2×(10x2n1)2×6= 2 \times (10x2^{n-1}) - 2 \times 6

Step 2: Simplify each term.

=20x2n112= 20x2^{n-1} - 12

So, the simplified expression is:

20x2n11220x2^{n-1} - 12

Would you like further explanation or assistance with any other questions?

Here are some related questions you might find interesting:

  1. What happens when you evaluate this expression for specific values of nn?
  2. How can you factor the expression 20x2n11220x2^{n-1} - 12?
  3. How would you differentiate this expression with respect to nn?
  4. How can you solve for nn if the expression equals a specific value?
  5. What is the behavior of the expression as nn increases?

Tip: Always distribute constants carefully in expressions with parentheses to avoid mistakes!

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Math Problem Analysis

Mathematical Concepts

Algebra
Exponentiation
Distribution

Formulas

Distributive property: a(b+c) = ab + ac

Theorems

Exponential properties
Distributive property

Suitable Grade Level

Grades 6-8