Question 1: Expand / Simplify the following:

(i)

Answer:

(ii)

Answer:

(iii)

Answer:

(iv)

Answer:

(v)

Answer:

(vi)

Answer:

(vii)

Answer:

Let

(viii)

Answer:

(ix)

Answer:

(x)

Answer:

(xi)

Answer:

(xii)

Answer:

(xiii)

Answer:

(xiv)

Answer:

(xv)

*Note: We will use the following identify: *

Answer:

(xvi)

Answer:

(xvii)

Answer:

(xviii)

Answer:

(xix)

Answer:

(xx)

Answer:

(xx)

Answer:

(xxi)

Answer:

*We will use the identity *

(xxii)

Answer:

*We will use the identity *

Therefore

(xxiii)

Answer:

*We will use the identity *

(xxiv)

Answer:

*We will use the identity *

(xxv)

Answer:

*We will use the identity *

Question 2: Evaluate the following identities:

(i)

Answer:

(ii)

Answer:

(iii)

Answer:

(iv)

Answer:

(v)

Answer:

(vi)

Answer:

*We will use the identity *

(vii)

Answer:

*We will use the identity *

(viii)

Answer:

*We will use the identity *

(ix)

Answer:

(x)

Answer:

*We will use the identity *

(xi)

Answer:

*We will use the identity *

(xii)

Answer:

*We will use the identity *

(xiii)

Answer:

*We are going to use this identity *

Question 3:

(i) If the number is more than number and the sum of the squares of and is , find the product of

Answer:

Therefore

(ii) If the number is less than the number and the sum if the square of and is , find

Answer:

(iii) If the sum of two numbers is and the sum of their cubes is , find the sum of their squares.

Answer:

Therefore