Power of Maths: Paper 1 – Section 2 EXERCISE 2
1. Factorise the following by taking out the HCF:
(a) 3x + 6y (b) x 2 + 3x (c) ab − ac (d) 4x 2 − 16xy (e) 3x 2 + 9x − 18 (f) 3x − 9y (g) 8a2 − 16a2b2 (h) 7x 2y 2 − 14x 2y (i) 3(x − 2y) − 5x(x − 2y) (j) m(a + b) − 3n(a + b)
2. Factorise the following by grouping: (a) ax 2 + 2ax + x + 2
(b) ax + by + ay + bx (c) ax − bx + ay − by (d) ab + 7a − 3b − 21 (e) 3np + 6nq – ap – 2aq (f) 2x 2 + 2x − 3xy − 3y (g) 2x − 6 − bx + 3b (h) x 2z − 2x 2 − 2y 2 + y 2z (i) 3x − 8y − 2 + 12xy (j) 21 − 3ax 2 − 14b + 2abx 2
3. Factorise the following trinomials: (a) x2 + 12x + 35 (b) x2 + 12x + 27 (c) x2 + 11x + 18 (d) x2 + 20x + 36 (e) x2 + 21x + 54 (f) x2 – 15x + 50 (g) x2 – x – 110 (h) x2 + x – 110 (i) x2 – 21x + 110 (j) x2 – 18x + 45
66
(k) 2x2 + 5x + 2 (l) 6x2 + 23x + 20 (m) 12x2 + 53x + 56 (n) 16x2 + 46x + 15 (o) 6x2 + 5x – 6 (p) 12x2 – x – 6 (q) 6x2 – 7x – 24 (r) 5x2 + 33x – 14 (s) 12x2 – 4x – 33 (t) 42x2 – 5x – 2
4. Factorise the following trinomials: (a) x 2 + 5xy + 6y 2 (b) x 2 + 9xy + 14y 2 (c) x 2 − 5xy + 6y 2 (d) x 2 + 5xy − 14y 2 (e) 10x 2 + 13x − 3 (f) 2x 2 − x − 15
(g) 7x 2 − 22xy + 3y 2 (h) 2a2 + ab − 3b2 (i) 30x 2 − 17x + 2 (j) b2x 2 + 2bcx + c2 (k) 4p2 − 4p + 1 (l) 18x2 + 25x – 3
5. Factorise the following differences of two squares:
(a) 4x 2 − 1 (b) 25x 2 − y 2 (c) 9x 2 − 16 (d) x 2 − a2b2
(e) 4m2 − 81n2 (f) (x + y)2 − z2 (g) (x + 1)2 − 9z2 (h) (Yoke)2 − (Thing)2
6. Factorise and hence evaluate the following without using your calculator:
(a) 512 − 492 (b) 532 − 472 (c) 1012 − 992 (d) 212 − 192
(e) 50⋅32 − 49⋅72 (f) 5042 − 4962 (g) 322 − 282
(h) 10⋅72 − 9⋅32
7. Factorise the following fully: (a) 2x 2 − 8
(b) 18a2 − 8b2 (c) 36x 2 + 15xy − 9y 2 (d) x 2y + 2x 2 − y − 2 (e) 28 − 7x 2 (f) 4x 2 − 24xy + 36y 2 (g) −2x 2 + 4xy − 2y 2 (h) (a + 1)2 − 9 (i) 16(x − 1)2 − 4 (j) 2a2 − 578
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