Find the value of a3-8b2-36ab-216 when a=2b+6
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Answered by
14
a³-8b²-36ab-216
a=2b+6
= (2b+6)³-8b²-36(2b+6)b-216
(a+b)³=a³+b³+3ab(a+b)
= (2b)³+(6)³+3(2b)(6)(2b+6)-8b²-72b²-216b-216
= 8b³+216+72b²+216b-8b²-72b²-216b-216
= 8b³+72b²-72b²-8b²+216b-216b+216-216
= 8b³-8b²
= 8b²(b-1)
= (8b)(b)(b-1)
a=2b+6
= (2b+6)³-8b²-36(2b+6)b-216
(a+b)³=a³+b³+3ab(a+b)
= (2b)³+(6)³+3(2b)(6)(2b+6)-8b²-72b²-216b-216
= 8b³+216+72b²+216b-8b²-72b²-216b-216
= 8b³+72b²-72b²-8b²+216b-216b+216-216
= 8b³-8b²
= 8b²(b-1)
= (8b)(b)(b-1)
Answered by
13
given a=2b+6
a-2b-6=0
We know ,if a+b+c=0 ,then
a^3+b^3+c^3-3abc=0
(a)^3-(2b)^3-(6)^3-3×a×(-2b)×(-6)=0
a^3-8b^3-216-36ab=0
the required value is zero (0)
In ques value of b is wrong it will be 8b^3 .you have written 8b^2
a-2b-6=0
We know ,if a+b+c=0 ,then
a^3+b^3+c^3-3abc=0
(a)^3-(2b)^3-(6)^3-3×a×(-2b)×(-6)=0
a^3-8b^3-216-36ab=0
the required value is zero (0)
In ques value of b is wrong it will be 8b^3 .you have written 8b^2
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