Question

Expand and simplify: 

Answer 1

$1.\\(n-2)(3n+7)+2n(2n+3)\\\\=n\cdot3n+n\cdot7-2\cdot3n-2\cdot7+2n\cdot2n+2n\cdot3\\\\=3n^2+7n-6n-14+4n^2+6n\\\\=7n^2+7n-14$

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$2.\\4x^2-25=(2x)^2-5^2=(2x-5)(2x+5)$

Answer 2

1.(n-2)(3n+7)+2n(2n+3)
We'll start with (n-2)(3n+7)
Use the FOIL method to simplify: First, Outside, Inside, Last. 
Multiply the first numbers of each bracket (n and 3n), the outside numbers (n and 7), the inside numbers (-2 and 3n) and the last numbers (-2 and 7)
F=  3n×n= 3n²
O= n×7= 7n
I= -2×3n= -6n
L= -2×7= -14
Add them together, you get 3n² + n -14.
The second part is 2n(2n+3)
Multiply both numbers inside the bracket by 2n
2n×2n= 4n²
3×2n= 6n
Add these terms with the previous ones
7n² + 7n -14
Because they all have a common factor of 7, we can represent the equation as 
7(n² + n -2)

2. 4x²-25
To factor this, we convert it into two expressions that we multiply together (like converting -9 into 3×-3)
2x × 2x= 4x²
5 × -5= -25
The answer is (2x+5)(2x-5)