GCSE Secondary Maths Age 13-17 - Algebra: Proof - Explained

The video tutorial explains a common exam question involving proving an expression is even for all positive integers. The instructor demonstrates expanding and subtracting brackets, simplifying the expression, and proving its evenness. An alternative method using the difference of squares is mentioned, along with the marking scheme for the solution.

What is the main goal of the problem discussed in the introduction?

• To find the value of N

• To prove an expression is odd

• To show an expression is even for all positive integers

• To solve for m and n

What is the result of expanding the expression (N + 3)^2?

• N^2 + 3N

• N^2 + 9

• N^2 + 6N + 9

• N^2 + 3N + 9

After expanding and simplifying, what expression do we get before factorization?

• N^2

• 6N

• 9N

• 12N

How is the expression 12N proven to be even?

• By showing it is a multiple of 3

• By factorizing it as 2 times 6N

• By adding 9 to it

• By subtracting 9 from it

What alternative method is mentioned for solving the problem?

• Using the quadratic formula

• Completing the square

• Difference of two squares

• Graphical method