• A variable is an unknown quantity that is prone to change with the context of a situation.
  Example: In the expression 2x+5, x is the variable.
• Constant is a quantity which has a fixed value. In the given example 2x+5, 5 is the constant.2 is the coefficient of the term 2x.
• 

No. of matchsticks used to make 1st square = 4

No. of matchsticks used to make 2nd square = 7

No. of matchsticks used to make 3rd square = 10

So, the pattern that we observe here is 3n + 1

Question: How many matchsticks will be used in the 50^th figure?

Answer: 3n + 1

3 × 50 + 1

= 151 matchsticks

• • Addition of $-5x^2+12xy$ and $7x^2+xy+7x$ is shown below:

  −5x²+12xy
  7x²+xy+7x
  __________
  2x²+13xy+7x
  __________

• • Subtraction of $-5x^2+12xy$ and $7x^2+xy+7x$ is shown below:

  −5x²+12xy
  −7x²+xy+7x
  __________

  12x²+11xy−7x
  __________

• If a natural number is denoted by n, then its successor is (n + 1).
  Example: Successor of $n=10$ is $n+1=11$.
• If a natural number is denoted by n, then 2n is an even number and (2n+1) is an odd number.
  Example: If $n=10$, then $2n=20$ is an even number and $2n+1=21$ is an odd number.