Factorise each of the following:
(i) 27y 3 + 125z 3
(ii) 64m3 – 343n 3
[ Hint : See Question 9. ]
Factorise each of the following:
(i) 27y 3 + 125z 3
(ii) 64m3 – 343n 3
[ Hint : See Question 9. ]
Solution and Explanation
(i) 27 y3 + 125 z3
= (3y)3 + (5z)3
= (3y + 5z) [(3y)2 + (5z)2 - (3y)(5z) ] [∵ a3 + b3 ]
= (a + b) (a2 + b2 - ab)
= (3y + 5z) [9y2 + 25z2 - 15yz]
(ii) 64m3 - 343n3
= (4m)3 - (7n)3
= (4m - 7n)[ (4m)2 + (7n)2 + (4m) (7n) ] [∵ a3 - b3 = (a - b) (a2 + b2 + 2ab) ]
= (4m - 7n) [16m2 + 49n2 + 28mn ]
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