Previously we have discussed about subtracting integers worksheet and In today's session we are going to discuss about Binomial theorem which comes under board of secondary education ap, It is defined as the algebraic expansion of the powers of a binomial expression . A binomial expression consists of two terms containing the positive or negative sign between them . For example: ( x + y ) or ( p / q2 ) - ( k / q 4 ) etc .
We can explain Binomial theorem as when the binomial expression have the power of ' n ' then it would be expand by the help of binomial theorem . It would be describe as ( 1 + a ) n = ∑ nr=0 c rn x r .
The above expansion can understand by an example as
( p + q ) 4 = p 4 + 4 p 3 q + 6 p 2 q 2 + 4 p q 3 + q 4 .In the example binomial coefficient in the expansion of ( p + q ) 4 are define as the coefficient in expansion of ( x + 1 )n are c r n or n c r or ( n r ) . for finding the values of the coefficient Pascal's triangle is used .
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
But by calculating Binomial Probability Formula for computing the numbers in the pascal triangle so that we can easily expand the formula easily without referring the triangle it is stated as :
( a + 1 ) n = c n n a n + c n n -1a n-1 + c n n -2 a n-2 + ….......+c n2 a 2 + c n1 a + c n0 .
In the next session we are going to discuss Perfect Square Trinomials
and Read more maths topics of different grades such as Properties of Numbers
in the upcoming sessions here.
.
We can explain Binomial theorem as when the binomial expression have the power of ' n ' then it would be expand by the help of binomial theorem . It would be describe as ( 1 + a ) n = ∑ nr=0 c rn x r .
The above expansion can understand by an example as
( p + q ) 4 = p 4 + 4 p 3 q + 6 p 2 q 2 + 4 p q 3 + q 4 .In the example binomial coefficient in the expansion of ( p + q ) 4 are define as the coefficient in expansion of ( x + 1 )n are c r n or n c r or ( n r ) . for finding the values of the coefficient Pascal's triangle is used .
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
But by calculating Binomial Probability Formula for computing the numbers in the pascal triangle so that we can easily expand the formula easily without referring the triangle it is stated as :
( a + 1 ) n = c n n a n + c n n -1a n-1 + c n n -2 a n-2 + ….......+c n2 a 2 + c n1 a + c n0 .
In the next session we are going to discuss Perfect Square Trinomials
and Read more maths topics of different grades such as Properties of Numbers
in the upcoming sessions here.
.
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