Explanation Given: ( m + n ) 6 A binomial is a polynomial which contains two terms. Algebraically, sum or difference of two monomials is a binomial. A triangular pattern of numbers, known as Pascal’s triangle is used to expand the binomials to any given power without direct multiplication. We start to generate Pascal’s triangle by writing down the number 1 . Then we write a new row with the number 1 twice. We then generate new rows to build a triangle of numbers. Each new row must begin and end with a 1 . The remaining numbers in each row are calculated by adding together the two numbers in the row above which lie above-left and above-right, So the vacant space is filled by 2 which is obtained by adding the 1 ' s . Now we can fill the vacant spaces in the fourth row by adding together the two numbers in the third row which lie above-left and above-right. We can continue in this way to build up the Pascal’s triangle with as many rows as we wish. Formula used: Pascal’s triangle with seven rows is as follows: Calculation: Description Step 1: Select the coefficients for the expansion of the given expression ( m + n ) 6 from the relevant seventh row of Pascal’s triangle. ( 1 , 6 , 15 , 20 , 15 , 6 , 1 ) Step 2: As we move from left to right, we have to decrease the power of m and increase the power of n . ( m + n ) 6 = 1 ( m ) 6 ( n ) 0 + 6 ( m ) 6 − 1 ( n ) 0 + 1 + 15 ( m ) 6 − 2 ( n ) 2 + 20 ( m ) 6 − 3 ( n ) 0 + 3 + 15 ( m ) 6 − 4 ( n ) 0 + 4

College Algebra with Modeling and Visualization with Mymathlab Access Code

5th Edition

ISBN: 9780321869418

Author: Gary K. Rockswold

Publisher: PEARSON

See similar textbooks

Videos

Question

Polygon with three sides, three angles, and three vertices. Based on the properties of each side, the types of triangles are scalene (triangle with three three different lengths and three different angles), isosceles (angle with two equal sides and two equal angles), and equilateral (three equal sides and three angles of 60°). The types of angles are acute (less than 90°); obtuse (greater than 90°); and right (90°).

Chapter 8.4, Problem 41E

To determine

The expanded form of given expression ${(m + n)}^{6}$ by using Pascal’s triangle.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 8.4, Problem 40E

Chapter 8.4, Problem 42E

Students have asked these similar questions

13) Let U = {j, k, l, m, n, o, p} be the universal set. Let V = {m, o,p), W = {l,o, k}, and X = {j,k). List the elements of the following sets and the cardinal number of each set. a) W° and n(W) b) (VUW) and n((V U W)') c) VUWUX and n(V U W UX) d) vnWnX and n(V WnX)

9) Use the Venn Diagram given below to determine the number elements in each of the following sets. a) n(A). b) n(A° UBC). U B oh a k gy ท W z r e t ་ C

10) Find n(K) given that n(T) = 7,n(KT) = 5,n(KUT) = 13.

Chapter 8 Solutions

College Algebra with Modeling and Visualization with Mymathlab Access Code

Ch. 8.1 - Prob. 1E Ch. 8.1 - Prob. 2E Ch. 8.1 - Prob. 3E Ch. 8.1 - Prob. 4E Ch. 8.1 - Prob. 5E Ch. 8.1 - Prob. 6E Ch. 8.1 - Prob. 7E Ch. 8.1 - Prob. 8E Ch. 8.1 - Prob. 9E Ch. 8.1 - Prob. 10E

Knowledge Booster

$Algebra$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, algebra and related others by exploring similar questions and additional content below.

The expanded form of given expression ( m + n ) 6 by using Pascal’s triangle .

Videos

The expanded form of given expression (m+n)6 by using Pascal’s triangle.

Want to see the full answer?

Chapter 8 Solutions

The expanded form of given expression ${(m + n)}^{6}$ by using Pascal’s triangle.