(a) Simplify : ((2a + b)^{2} – (b – 2a)^{2})
(b) Given that (S = Ksqrt{m^{2} + n^{2}}); (i) make m the subject of the relations ; (ii) if S = 12.2, K = 0.02 and n = 1.1, find, correct to the nearest whole number, the positive value of m.
Explanation
(a) ((2a + b)^{2} – (b – 2a)^{2})
Using the method of difference of two squares,
((2a + b)^{2} – (b – 2a)^{2} = ((2a + b) + (b – 2a))((2a + b) – (b – 2a)))
= ((2b)(4a))
= (8ab).
(b)(i) (S = Ksqrt{m^{2} + n^{2}})
(S^{2} = K^{2}[m^{2} + n^{2}])
(frac{S^{2}}{K^{2}} = m^{2} + n^{2})
(m^{2} = frac{S^{2}}{K^{2}} – n^{2})
(m = sqrt{frac{S^{2}}{K^{2}} – n^{2}})
(ii) When S = 12.2, K = 0.02, n = 1.1
(m = sqrt{frac{12.2^{2}}{0.02^{2}} – (1.1^{2})})
(m = sqrt{frac{148.84}{0.0004} – 1.21})
(m = sqrt{372,098.79})
= (609.999 approxeq 610)