C.Reduce to simplest form
(i)a^2 b^3 c^2
abc(ii)(a^2 )^3 c^12
ab^2(iii)ba^12 b^7 c^4
(a^2 b^4 c^6 )^1 /^2(iv)(a^3 )^4 c^12
b−^3 c^10 a−^1 b^2D.Simplify the following expressions
(i) b^2 a^2 b^3 ab^3 (ii)t^3 xy
x^2 yt(iii)(x^2 )^4 y^7 /^2
(x^6 )^1 /^3
√
y2.3.13 The binomial theorem
➤➤
40 71➤A.Write down the coefficients ofx^4 in the following expansions
(i) ( 1 +x)^7 (ii) ( 1 + 3 x)^6 (iii) ( 1 − 2 x)^5(iv) ( 3 − 2 x)^8 (v) ( 3 x+ 2 y)^6B. Expand by the binomial theorem
(i) ( 1 − 2 x)^7 (ii) (a+b)^6 (iii) ( 2 x+ 3 y)^5(iv) ( 2 − 3 x)^6 (v) ( 3 s− 2 t)^5C.Evaluate, without using a calculator:
(i) ( 1 +√
2 )^3 +( 1 −√
2 )^3 (ii) ( 2 +√
3 )^4 +( 2 −√
3 )^4D.Use the binomial theorem to evaluate to three decimal places:
(i) ( 1. 01 )^10 (ii) ( 0. 998 )^8Hint: write 1. 01 = 1 + 0 .01 and 0. 998 = 1 − 0 .002.
2.4 Applications
1.The time behaviour of a source free resistor (R)-inductor (L)-capacitor (C) series circuit
can be described by a particulardifferential equation:
d^2 V
dt^2+R
LdV
dt+1
LCV= 0