on Problems Revision Material - Week 3
1. Multiply out the following, collecting like terms where possible. (i) (iii) - ab(a + 3b - c - 1); - a(a + b); (ii) (2 - ab)(-c - 1); (iv) (a - b)(2a + b)(a - 2b); - 3(3x + 4y); - (p + 1)(p - 1);
(v) (x - 3)(x + 4)(-x - 4); (vi) (vii) - 1(p - 1); (viii)
(ix) (-p + 1)(q - 1)(-p);
(x) (a - b)(2x - 3y)2 ;
2. Write the following as a single fraction, collecting like terms in the numerator. (i) (iii) (v) (vii) (ix) 1 1 + ; p q 1 1 + ; p+1 q-1 p-q pq - ; p+q q-1 3 p + 2 ; (p + 1)2 p - 1 3 p 1 + - ; p+1 p-1 p (ii) (iv) (vi) (viii) (x) 1 1 - ; p q 1 1 - ; p+1 q-1 p 5p - ; q(p + 1) q - 1 (p + 2q)q (p - 2q)p - ; p+1 q-1 (p + 2q)q (p - 2q)p 3p - + . p+1 q-1 q
3. Factorize and simplify the following as much as possible. (i) (iii) (v) (vii) (ix) a2 + 2ab + b2 ; a+b a2 c2 + 2abc + b2 ; ac + b 36x2 - 49y 2 ; 36x2 - 84xy + 49y 2 2x2 - 2y 2 ; (3x2 - 3y 2 )(x2 - 2xy + y 2 ) r 4 - t4 ; r4 - 2r2 t2 + t4 (ii) (iv) (vi) (viii) (x) a2 - 2ab + b2 ; a-b ab2 c a ; + 2abc + acb2
180x2 - 245y 2 ; 36x2 - 84xy + 49y 2 a2 + 2ab + b2 ; 3a + 3b 48a3 b8 c2 k 5 - 36a4 b3 c9 d2 k 2 - 66a3 b2 c4 ; 72a10 b4 c3 + 144a7 b7 c3 + 72a4 b10 c3
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MAS001, Problems on Revision Material
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Solutions Problems to on Revision Material
Check your own answers below. If you can't see how to get there, just ask! 1. We have the following solutions. (i) (iii) (v) (vii) (ix) (x) - a2 b - 3 a b2 + a b c + a b. (ii) a b c + a b - 2 c - 2. 2 - a - a b. (iv) 2 a3 - 5 a2 b + a b2 + 2 b3 . - x3 - 5 x2 + 8 x + 48. (vi) - 9 x - 12 y. - p + 1. (viii) - p2 + 1. p2 q - p2 - p q + p. 4 a x2 - 12 a x y + 9 a y 2 - 4 b x2 + 12 b x y - 9 b y 2 .
2. We have the following solutions. (i) (iii) (v) (vii) (ix) (x) q+p . pq q+p . (p + 1) (q - 1) -q 2 - pq 2 - p2 q + pq + q - p . (q + p) (q - 1) p2 + 4 p - 3 . (p2 - 1) (p + 1) p3 + 3 p2 - 3 p + 1 . p (p2 - 1) q 3 p + p q 2 + 2 q 4 - 2 q 3 - p3 q + 2 p2 q + 2 p2 q 2 - 3 p2 + 3 p q - 3...