Theory question 101
Algebraic Expressions(a) Simplify (2a + b)2 − (b − 2a)2
(b) Given that S = K√(m2 + n2); (i) make m the subject of the relation; (ii) if S = 12.2, K = 0.02 and n = 1.1, find, correct to the nearest whole number, the positive value of m.
Show the model answer
Model answer
(a) Difference of two squares: [(2a + b) − (b − 2a)][(2a + b) + (b − 2a)] = 4a × 2b = 8ab.
(b)(i) S/K = √(m2 + n2), so m2 = S2/K2 − n2 and m = √(S2/K2 − n2).
(ii) S/K = 12.2/0.02 = 610. m = √(372100 − 1.21) ≈ 610.
Explanation
Square both sides to remove the root, then isolate m².