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= 3(x + 5y)(x – 5y)<br />
The difference of two squares can be used to evaluate some expressions that involve<br />
numbers in a faster way.<br />
Example<br />
Evaluate:<br />
(a) 99 2 – 1 (b) 8.49 2 – 1.51 2<br />
(c) 1012 × 988<br />
Solutions<br />
(a) 99 2 – 1 = 99 2 - 1 2<br />
= (99 – 1)(99 + 1)<br />
= 98 × 100<br />
= 9800<br />
(b) 8.49 2 – 1.51 2 = (8.49 – 1.51)(8.49 + 1.51)<br />
= 6.98 × 10<br />
= 69.8<br />
(c) 1,012 × 988 = (1,000 + 12)(1,000 – 12)<br />
= 1,000 2 – 12 2<br />
= 1,000,000 – 144<br />
= 999,856<br />
Exercise<br />
1. Factorize:<br />
(a) x 2 – 2 2 (b) x 2 – 5 2<br />
(c) 7 2 – n 2 (d) 1 – t 2<br />
(e) (3a) 2 – 1 (f) 4c 2 – 25 2<br />
(g) 25 – 49r 2 (h) p 2 – 36q 2<br />
(i) p 2 q 2 – 1 (j) 48a 2 – 3t 2<br />
(k) 72m 2 – 2 (l) 4p 2 - 4q 2<br />
(m) x 4 – 1 (n) a 3 b – ab 3<br />
(o) nu 2 – nv 2<br />
2. Calculate:<br />
(a) 78.3 2 – 21.7 2 (b) 923 2 – 77 2<br />
(c) 0.843 2 – 0.157 2 (d) 75 2 – 25 2
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