Question : What is the simplified value of $(2 + 1) (2^{2} + 1) (2^{4} + 1) (2^{8} + 1)$ ?
Option 1: $2^{8} - 1$
Option 2: $2^{16} - 1$
Option 3: $2^{32} - 1$
Option 4: $2^{64} - 1$

Question

Question : What is the simplified value of $(3 + 1) (3^{2} + 1) (3^{4} + 1) (3^{8} + 1) (3^{16} + 1)$ ?
Option 1: $\frac{(3^{32} - 1)}{2}$
Option 2: $\frac{(3^{16} - 1)}{2}$
Option 3: $\frac{(3^{64} - 1)}{2}$
Option 4: $\frac{(3^{128} - 1)}{2}$

8 Views

Answer 1

Correct Answer: $2^{16} - 1$

Solution : Given: $(2 + 1) (2^{2} + 1) (2^{4} + 1) (2^{8} + 1)$
Multiplying (2 – 1) = 1 in the equation, we get:
$(2 - 1) (2 + 1) (2^{2} + 1) (2^{4} + 1) (2^{8} + 1)$
= $(2^{2} - 1) (2^{2} + 1) (2^{4} + 1) (2^{8} + 1)$
= $(2^{4} - 1) (2^{4} + 1) (2^{8} + 1)$
= $(2^{8} - 1) (2^{8} + 1)$
= $(2^{16} - 1)$
Hence, the correct answer is $(2^{16} - 1)$ .

Exams

Colleges

Predictors

Resources

Quick links

Exams

Colleges & Courses

Predictors

Resources

Exams

Colleges

Predictors & E-Books

Resources

Engineering Preparation

Medical Preparation

Law Preparation

MBA Preparation

Exams

Colleges

Resources

Exams

Colleges

Predictors & Articles

Resources

Exams

Colleges

Predictors

Resources

Exams

Colleges

Upcoming Events

Resources

Exams

Colleges

Resources

Quick Links

Top Streams

Specializations

Resources

Top Providers

Exams

Colleges

Resources

Diploma Colleges

Exams

Colleges

Resources

Exams

Resources

Top Courses & Careers

Colleges

Exams

Upcoming Events

Resources

Other Exams

Exams

Colleges

Top Countries

Resources

Exams

Top Schools

Products & Resources

NCERT Study Material

Popular Searches

Question : What is the simplified value of (2+1)(22+1)(24+1)(28+1)?Option 1: 28−1Option 2: 216−1Option 3: 232−1Option 4: 264−1

Related Questions

Know More about

Upcoming Exams

Trending Articles around SSC CPO

Download Careers360 App

All this at the convenience of your phone

Scan and download the app

Sign In/Sign Up

Question : What is the simplified value of $(2 + 1) (2^{2} + 1) (2^{4} + 1) (2^{8} + 1)$ ?
Option 1: $2^{8} - 1$
Option 2: $2^{16} - 1$
Option 3: $2^{32} - 1$
Option 4: $2^{64} - 1$