Algebra 3

3 marks · Hard

Write down an algebraic identity involving squares that is always true for any value of , and show why it is always true by expanding or simplifying it.

Work this out on paper, then compare with the answer and worked solution below. With a free account you can submit written answers for marking.

Show answer

(x + y)^2 = x^2 + 2xy + y^2, and expanding (x+y)(x+y) shows this is always true for any x, y.

Must show: States a correct identity involving squares (e.g., (x + y)^2 = x^2 + 2xy + y^2), Expands the bracket or provides reason why true, Explains why true for any x, y

Also accept: (x - y)^2 = x^2 - 2xy + y^2, with correct demonstration; (x + a)(x - a) = x^2 - a^2, with expansion and justification

Common mistakes: Confusing identity with equation (using =) rather than always-true form; Providing an expression, not an identity; Incorrect expansion

Show mark scheme and worked solution

Marking points

B1 · 1 mark · Writes down a valid algebraic identity involving squares (e.g., (x + y)^2 = x^2 + 2xy + y^2)

M1 · 1 mark · Expands the bracket or shows correct working toward checking the identity

A1 · 1 mark · Clearly states/explains why the identity is always true, for any x (or x and y)

Worked solution

One valid identity:

This can be shown by expanding:

This expansion is always true for any values of x and y.