Trinomial Squaring Twice

In elementary algebra, a trinomial is a polynomial consisting of three terms or monomials.(source : WIKIPEDIA)
The trinomial must be one of the following form .
Examples for trinomial:    
1.  x + y + z , where x , y, z are variables.
2. 2xy + 3x + 4y, Where x, y are variables.
3. x²+2x-7, where x is variable.
4. ax + by + c = 0 , Where a,b,c are constants and x,y are variables.
In the following section we are going to see some solved problems and practice problems on trinomial squaring twice .

Solved problems on trinomial squaring twice:

Trinomial squaring twice problem 1:
Solve by squaring twice (2x + 5y + 6)⁴
Solution:
Given , (2x + 5y + 6)⁴
We can write it as , (2x + 5y + 6)⁴  = (2x + 5y + 6)^{2^2}               
                                                             = (2x + 5y + 6)² × (2x + 5y + 6)²
Let us take (2x + 5y + 6)²
We can apply the following formula to square the trinomial,
(a+b+c)² = ( a² + b² + c² + 2ab + 2bc + 2ca )
(2x + 5y + 6)² = (4x² + 25 y² + 36 + 20xy + 60x + 24x)
(2x + 5y + 6)² × (2x + 5y + 6)² = (4x² + 25 y² + 36 + 20xy + 60x + 24x) × (4x² + 25 y² + 36 + 20xy + 60x + 24x)
Answer: 2x + 5y + 6)⁴ =   (4x² + 25 y² + 36 + 20xy + 60x + 24x) × (4x² + 25 y² + 36 + 20xy + 60x + 24x) 

Trinomial squaring twice problem 2:
Find the trinomial by squaring (3x +2).
Solution:
Given (3x +2)
We can get the trinomial by squaring the given binomial.
(3x+2)² = (3x + 2) ( 3x + 2)
              = 3x(3x + 2) + 2( 3x+2 )
              = 9x² + 6x + 6x + 4
              = 9x² + 12x + 4
Answer: (3x+2)² =  9x² + 12x + 4

Trinomial squaring twice problem 3 :
Factor the trinomial 2x²- 22 x + 48
Solution:
Given 2x²- 22 x + 48
Divide by 2 ,We get  x²- 11x + 24
                                                                     24   (product)
                                                                     /  \    
                                                                 - 8   - 3 
                                                                    \   / 
                                                                    - 11     (sum)
Factors:  (x-8) and (x-3).
Verification:
(x-8) (x-3)  = x(x-8) -3(x-8)
                = x²-8x -3x+24
(x-8) (x-3)  = x² -11x + 24

Practice problems on trinomial squaring twice:

Problems:
1. Find the trinomial by squaring (5x + 6 )
2.Find the trinomial by squaring (x-8)
Answers:
1.25x² + 60x + 36
2. x² -16x + 64