2.3.11 Properties of quadratic expressions and equations
A. (i) (x− 1 )(x+ 2 ) (ii) (x+ 3 )^2 (iii) (x− 9 )(x+ 9 )
(iv) (x+ 3 )( 2 x− 1 ) (v) 2x(x− 4 )B. (i) 1,− 2 (ii) − 3 ( 2 ×) (iii) ± 9
(iv) −3,^12 (v) 0, 4C. (i) (x+ 1 )^2 + 1 (ii) (x− 3 )^2 + 22 (iii) 4
(
x+^12) 2
− 32
(iv) 4(
x−^12) 2
− 1D.(i) Minimum of 3 whenx=− 1
(ii) Maximum of 17 whenx=−^12E. (i) −1,− 2 (ii) 2,^12 (iii)^23 ,3
(iv) −2,− 8 (v) 2,−4(vi)−1,^13F. 2
G. (i) (a)−3 (b) 2 (ii) (a)
5
2(b) 1 (iii) (a)11
3(b) 2(iv) (a)−10 (b) 16 (v) (a)−2(b)−8(vi)(a)^23 (b)−^132.3.12 Powers and indices for algebraic expressions
A.(i)a^6 (ii)a^6 (iii)a^2 (iv)a^8 (v)a^7 (vi)a−^1 (vii)a^8 (viii) 1
B. (i) 13 (ii) 5 (iii) 9 (iv) 11
C.(i)ab^2 c (ii)a^5 b−^2 c^12 (iii)a^11 b^6 c (iv)a^13 bc^2
D.(i)a^3 b^8 (ii)
t^2
x=t^2 x−^1 (iii)x^6 y^32.3.13 The binomial theorem
A. (i) 35 (ii) 1215 (iii) 80
(iv) 90720 (v) 4860B. (i) 1− 14 x+ 84 x^2 − 280 x^3 + 560 x^4 − 672 x^5 + 448 x^6 − 128 x^7
(ii) a^6 + 6 a^5 b+ 15 a^4 b^2 + 20 a^3 b^3 + 15 a^2 b^4 + 6 ab^5 +b^6(iii) 32x^5 + 240 x^4 y+ 720 x^3 y^2 + 1080 x^2 y^3 + 810 xy^4 + 243 y^5