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Solution :

`p^2q-pq-pr^2+r^2`<br>
`pq(p-1)-r^2(p-1)`<br>
`(pq-r^2)(p-1)`.**Definition of algebraic expressions**

**Operations on algebric expressions - Addition, Subtraction, Multiplication and Division**

**Some Important Identities - (i) `(a+b)^2 = a^2 + 2ab + b^2` (ii) `(a-b)^2 = a^2 - 2ab + b^2`**

**Important Identity - `(a-b)(a+b) = a^2 - b^2`**

**Important Identitiy `(x+a)(x+b) = x^2+(a+b)x+ab`**

**Expand each of the following (i) `(2x+5y)^2` (ii) `(x-3y)^2` (iii) `(x+5)(x-3)`**

**Evaluate each of the following by using Identities - (i) 103 x 97 (ii) 103 x 103 (iii) 97 x 97 (iv) 105 + 106**

**Simplify : `(a-1/a)(a+1/a)(a^2+1/a^2)(a^4+1/a^4)(a^8+1/a^8)`**

**If `x+1/x = 4`; Find (i) `x^2+1/x^2` (ii) `x^4 + 1/x^4`**

**If `x^2+1/x^2` = 5 is given then find the value of (i) `x+1/x` (ii) ` x-1/x`**