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

The video tutorial explains how to prove algebraically that the expression n^2 - (n-2)^2 is always even. It begins by expanding the expression, simplifying it by collecting like terms, and then factorizing it to show that it is always even. The tutorial emphasizes careful handling of minus signs and provides a breakdown of the marking scheme for the problem.

What is the initial expression that needs to be proven as even?

• N^2 - (N-2)^2

• (N-2)^2 + 2N

• N^2 + (N-2)^2

• N^2 - 2N

When expanding (N-2)^2, what is the correct expression obtained?

• N^2 - 4N - 4

• N^2 - 2N + 4

• N^2 + 4N + 4

• N^2 - 4N + 4

What is the result of simplifying the expression after expansion and collecting like terms?

• 2N - 6

• 2N + 6

• 4N + 6

• 4N - 6

Why is the expression always even after factorization?

• Because it is multiplied by 2

• Because it is multiplied by 3

• Because it is multiplied by 4

• Because it is multiplied by 5

What is one key point to remember when expanding and simplifying expressions?

• Be careful with negative signs

• Always add terms

• Ignore like terms

• Multiply all terms by 3