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06/07/2021 11:59 am
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Factorize each of the following:
(i) 27y3 + 125z3
(ii) 64m3 – 343n3
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06/07/2021 12:00 pm
(i) 27y3 + 125z3
The expression, 27y3+125z3 can be written as (3y)3+(5z)3
27y3+125z3 = (3y)3+(5z)3
We know that, x3+y3 = (x + y)(x2–xy+y2)
27y3+125z3 = (3y)3+(5z)3
= (3y+5z)[(3y)2–(3y)(5z)+(5z)2]
= (3y+5z)(9y2–15yz+25z2)
(ii) 64m3 – 343n3
The expression, 64m3–343n3can be written as (4m)3–(7n)3
64m3–343n3 = (4m)3–(7n)3
We know that, x3–y3 = (x–y)(x2+xy+y2)
64m3–343n3 = (4m)3–(7n)3
= (4m-7n)[(4m)2+(4m)(7n)+(7n)2]
= (4m-7n)(16m2+28mn+49n2)