Perfect Square Trinomials

Hello friends. Previously we have discussed about consecutive exterior angles and In today's session we are going to discuss about Perfect Square Trinomials which comes under school secondary board of andhra pradesh,

Perfect Square:  It is a number whose square root is a rational number.
Example:
121 = 11²
121 is a perfect square of 11 which is a rational number.
0, 1, 4, 9, 16, 25, 36, 49, 64, 81, etc all these are the perfect squares.
The perfect squares can also be in the form of p/q
Example:
9/49, 16/81, etc are also perfect squares.
Trinomials: In polynomial expression there can be many terms in an equation but in factoring trinomials there must have exactly three terms connected by a plus or a minus sign.
Example:
4m² – 3m + 2
m² + 7m – 8
Perfect Square Trinomial: It can be represented by the following formula x² ± 2xy ± y²  (in another way we can see this formula as the square of the binomials); such trinomials are called perfect square trinomials.  Perfect square trinomials can be formed when a binomial is multiplied by itself.
(x ±y)² = x² ± 2xy ± y²
X² + 18X + 9is an example of perfect square trinomials, it can be shown in the form of (x + 3)²
Let’s see what the outcome is when we square any binomial, take (x + y)
(x +y)² =(x + y)(x + y) = x² + 2xy + y²
The square of a binomial expression gives rise to the following three terms:
1.       x²  as Square of the first term of binomial
2.       2xy as Twice the product of two terms
3.       y² as Square of the second term of binomial
It going to be the same if there is minus sign in place of plus sign.
But we have to check first whether a trinomial is a perfect square trinomial or not.
In the next session we are going to discuss factor algebra calculator
and if anyone want to know about Binary Numbers then they can refer to Internet and text books for understanding it more precisely.
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Binomial Theorem

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 = ∑ ⁿ_r=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 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 -1}a ^n-1 + c ⁿ _{n -2} a ^n-2 + ….......+c ⁿ₂ a ² + c ⁿ₁ a + c ⁿ_{0 .}
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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