Genius Maker  School software  Maths softwarePOLYNOMIAL EXPANSION(PASCAL'S TRIANGLE) 
The Polynomial Expansion is a mathematics software for finding out the expansion coefficients for each term in the expansion of (a+b)^{n} for any user defined value of " n ". In other words, this software can be used as a tool to find out the values in any row of the Pascal's triangle.
 Open Genius Maker software and click "Polynomial Expansion" button. It opens the Polynomial Expansion window as shown above.
 It asks you to enter the value for " n ". By default it shows a sample value.
EXAMPLE 1:
 Enter the value of n as " 3 ".
 Click "Solve" button.
 The result box displays the following
Coef. of term 1, a³ b° is 1
Coef. of term 2, a² b¹ is 3
Coef. of term 3, a¹ b² is 3
Coef. of term 4, a° b³ is 1 This implies the following Polynomial expansion.
(a+b)^{3} = a³ b° + 3 a² b¹ + 3 a¹ b² + a° b³
 It also implies that the fourth row of Pascal's triangle is
1 3 3 1
EXAMPLE 2:
 Enter the value of n as " 7 ".
 Click "Solve" button.
 The result box displays the following
Coef. of term 1, a^7 b° is 1
Coef. of term 2, a^6 b¹ is 7
Coef. of term 3, a^5 b² is 21
Coef. of term 4, a^4 b³ is 35
Coef. of term 5, a³ b^4 is 35
Coef. of term 6, a² b^5 is 21
Coef. of term 7, a¹ b^6 is 7
Coef. of term 8, a° b^7 is 1 This implies the following Polynomial expansion.
(a+b)^{7} = a^{7 }+ 7 a^{6} b + 21 a^{5} b^{2} + 35 a^{4} b^{3} + 35 a^{3} b^{4} + 21 a^{2} b^{5} + 7 a b^{6} + b^{7}
It also implies that the eighth row of Pascal's triangle is
1 7 21 35 35 21 7 1
EXAMPLE 3:
 QUESTION:
What is the expansion coefficient of term a^{21} b^{8 } in the expansion of (a+b)^{29 } ?^{ }
 SOLUTION:
Enter the value of n as " 29 ".
 Click "Solve" button.
 Scroll the result box to the line where a^{21} b^{8 }is displayed. It reads as
Coef. of term 9, a^21 b^8 is 4292145
 Hence the expansion coefficient of term a^{21} b^{8 } in the polynomial expansion of (a+b)^{29 }is 4292145
The Pascal Triangle is a triangle of numbers arranged in such a way that the rows of the triangle are the expansion coefficients of (a+b)^{n} .
The first row is the expansion coefficient of (a+b)^{n }with n = 0.
The second row is the expansion coefficient of (a+b)^{n }with n = 1.
The third row is the expansion coefficient of (a+b)^{n }with n = 2.
..... and so on.
The numbers constructed are arranged as shown below, which is Pascal's triangle.
1
1 1
1 2 1
1 3 3 1
1 4 6 4 1
1 5 10 10 5 1
1 6 15 20 15 6 1
1 7 21 35 35 21 7 1
1 8 28 56 70 56 28 8 1
1 9 36 84 126 126 84 36 9 1
1 10 45 120 210 252 210 120 45 10 1
1 11 55 165 330 462 462 330 165 55 11 1
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