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
Question 4:
(i) If
, find (a)
(b)
Answer:
(a)
(b)
(ii) If
, find (a)
(b)
(c)
Answer:
(a)
(b) Since
Therefore
(c)
Therefore
(iii) If
, find (a)
(b)
Answer:
(a)
(b)
(iv)
, find the value of
Answer:
(v)
, find the value of
Answer:
(vi)
, find the value of
and
Answer:
Now
(vii) If
, find the value of
Answer:
(viii) If
, find the value of
Answer:
(ix) If , find the value of
Answer:
(x) If
, find the value of
Answer:
Now
(xi) If
, find the value of (a)
(b)
(c)
Answer:
(a)
(b)
(c)
(xii) If , find the values of (a)
(b)
Answer:
(a)
(b)
(xiii) If find the value of
Answer:
Therefore
(xiv) If and
, find the value of
Answer:
Given: and
We know:
(xv) If and
, find the value of
Answer:
Given: and
We know:
(xvi) If and
, find the value of
Answer:
Given: and
We know:
(xvii) If and
, find the value of
Answer:
Given: and
We know:
(xviii) If
, find the value of
Answer:
Given
If
Similarly, if
Then
(xix) If
, find the value of
Answer:
Given
If
Similarly, if
Then
(xx) If
, find the value of
Answer:
Given
Now
If
Similarly, if
Then
(xxi) If and
, find the value of
Answer:
Given and
(xxii) If and
, find the value of
Answer:
Given and
(xxiii)
, find
Answer:
If
(xxiv)
, find
Answer:
If
(xxv)
, find
Answer:
Given
If
Similarly, if
Then
(xxvi)
, find
Answer:
Given
Now
Similarly, if
Then
(xxvii)
, find
Answer:
Given
Given
If
Similarly, if
Then
(xxviii)
, find
,
and
Answer:
Now
(xxix)
, find
,
and
Answer:
Given
Therefore
If
Similarly, if
Then
(xxx)
, find
Answer: