Explanation Given: ( 3 x 2 + y 3 ) 4 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 . 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 ( 3 x 2 + y 3 ) 4 from the relevant fifth row of Pascal’s triangle. ( 1 , 4 , 6 , 4 , 1 ) Step 2: As we move from left to right, we have to decrease the power of 3 x 2 and increase the power of y 3 . ( 3 x 2 + y 3 ) 4 = 1 ( 3 x 2 ) 4 ( y 3 ) 0 + 4 ( 3 x 2 ) 4 − 1 ( y 3 ) 0 + 1 + 6 ( 3 x 2 ) 4 − 2 ( y 3 ) 0 + 2 + 4 ( 3 x 2 ) 4 − 3 ( y 3 ) 0 + 3 + 1 ( 3 x 2 ) 4 − 4 ( y 3 ) 0 + 4 ( 3 x 2 + y 3

6th Edition

ISBN: 9780134418117

Author: Rockswold

Publisher: PEARSON CO

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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 44E

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The expanded form of given expression ${(3 x^{2} + y^{3})}^{4}$ by using Pascal’s triangle.

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Chapter 8.4, Problem 43E

Chapter 8.4, Problem 45E

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Rolling a...Ch. 8.6 - Prob. 12E Ch. 8.6 - Prob. 13E Ch. 8.6 - Prob. 14E Ch. 8.6 - Prob. 15E Ch. 8.6 - Prob. 16E Ch. 8.6 - Find the probability of each event. 17. Randomly...Ch. 8.6 - Prob. 18E Ch. 8.6 - Prob. 19E Ch. 8.6 - Prob. 20E Ch. 8.6 - Prob. 21E Ch. 8.6 - Prob. 22E Ch. 8.6 - Prob. 23E Ch. 8.6 - Prob. 24E Ch. 8.6 - Prob. 25E Ch. 8.6 - Prob. 26E Ch. 8.6 - Prob. 27E Ch. 8.6 - Prob. 28E Ch. 8.6 - Prob. 29E Ch. 8.6 - Prob. 30E Ch. 8.6 - Prob. 31E Ch. 8.6 - Prob. 32E Ch. 8.6 - Prob. 33E Ch. 8.6 - Prob. 34E Ch. 8.6 - Prob. 35E Ch. 8.6 - Prob. 36E Ch. 8.6 - Prob. 37E Ch. 8.6 - Prob. 38E Ch. 8.6 - Prob. 39E Ch. 8.6 - Prob. 40E Ch. 8.6 - Entrance Exams A group of students is preparing...Ch. 8.6 - Prob. 42E Ch. 8.6 - Pinterest Categories The table shows the most...Ch. 8.6 - Prob. 44E Ch. 8.6 - Prob. 45E Ch. 8.6 - 46. 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Chapter 8 Solutions

The expanded form of given expression ${(3 x^{2} + y^{3})}^{4}$ by using Pascal’s triangle.