If x - 1/x = 4, find the value of x^2 + 1/x^2. (Hint: x^2 + 1/x^2 = (x - 1/x )^2 + 2.)

18. (x - 1/x )^2 = x^2 - 2 + 1/x^2, so x^2 + 1/x^2 = (x - 1/x )^2 + 2 = 4^2 + 2 = 16 + 2 = 18.

If $x - \frac{1}{x} = 4$ , find the value of $x^{2} + \frac{1}{x ^{2}}$ . (Hint: $x^{2} + \frac{1}{x ^{2}} = (x - \frac{1}{x})^{2} + 2.$ )

Class 8Algebraic Expressions and IdentitiesAlgebra

(x - \frac{1}{x})^{2} = x^{2} - 2 + \frac{1}{x ^{2}}, so x^{2} + \frac{1}{x ^{2}} = (x - \frac{1}{x})^{2} + 2 = 4^{2} + 2 = 16 + 2 = 18

Answer: D) 18

Combine **like terms only** — same variables and same powers.

Example:

(3 x^{2} + 4 x - 2) + (5 x^{2} - 7 x + 8) = (3 x^{2} + 5 x^{2}) + (4 x - 7 x) + (- 2 + 8) = 8 x^{2} - 3 x + 6

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For subtraction, distribute the minus sign first:

(3 x^{2} + 4 x) - (x^{2} - 2 x) = 3 x^{2} + 4 x - x^{2} + 2 x = 2 x^{2} + 6 x

Don't just memorise the answer — build a daily practice habit.