Add the following expressions:
- (a)p2 – 7pq – q2 and – 3p2 – 2pq + 7q2
- (b)x3 – x2y – xy2 – y3 and x3 – 2x2y + 3xy2 + 4y
- (c)ab + bc + ca and – bc – ca – ab
- (d)p2 – q + r, q2 – r + p and r2 – p + q (e) x3y2 + x2y3 +3y4 and x4 + 3x2y3 + 4y4 (f) p2qr + pq2r + pqr2 and – 3pq2r –2pqr2 (g) uv – vw, vw – wu and wu – uv (h) a2 + 3ab – bc, b2 + 3bc – ca and c2 + 3ca – ab 5 4 5 1 9 (i) p + 2 p 2 + ; –17 p + p 2 and p 5 – p 3 +7 8 8 8 8 (j) t – t2 – t3 – 14; 15t3 + 13 + 9t – 8t2; 12t2 – 19 – 24t and 4t – 9t2 + 19t3 The common properties of the four sequences of patterns on previous page are: • the first figure has 5 elements (squares, dots, stars or bars); • with each step in the row of figures, the number of elements grows by 4. So, the four sequences of patterns correspond to the same number sequence. Remark: To reach the 50th number in the strip, you need 49 steps. So take n = 49 and you find the 50th number: 5 + 4 × 49 = 201. 15-04-2018
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(a) p2 – 7pq – q2 and – 3p2 – 2pq + 7q2
(b) x3 – x2y – xy2 – y3 and x3 – 2x2y + 3xy2 + 4y
(c) ab + bc + ca and – bc – ca – ab
(d) p2 – q + r, q2 – r + p and r2 – p + q (e) x3y2 + x2y3 +3y4 and x4 + 3x2y3 + 4y4 (f) p2qr + pq2r + pqr2 and – 3pq2r –2pqr2 (g) uv – vw, vw – wu and wu – uv (h) a2 + 3ab – bc, b2 + 3bc – ca and c2 + 3ca – ab 5 4 5 1 9 (i) p + 2 p 2 + ; –17 p + p 2 and p 5 – p 3 +7 8 8 8 8 (j) t – t2 – t3 – 14; 15t3 + 13 + 9t – 8t2; 12t2 – 19 – 24t and 4t – 9t2 + 19t3 The common properties of the four sequences of patterns on previous page are: • the first figure has 5 elements (squares, dots, stars or bars); • with each step in the row of figures, the number of elements grows by 4. So, the four sequences of patterns correspond to the same number sequence. Remark: To reach the 50th number in the strip, you need 49 steps. So take n = 49 and you find the 50th number: 5 + 4 × 49 = 201. 15-04-2018