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Question Number 217163 by hardmath last updated on 03/Mar/25
If a+b=b+c=4 find: a^2 −b^2 −8c = ?
$$\mathrm{If}\:\:\:\mathrm{a}+\mathrm{b}=\mathrm{b}+\mathrm{c}=\mathrm{4} \\ $$$$\mathrm{find}:\:\:\:\mathrm{a}^{\mathrm{2}} −\mathrm{b}^{\mathrm{2}} −\mathrm{8c}\:=\:? \\ $$
Answered by AntonCWX08 last updated on 03/Mar/25
a+b=b+c⇒a=c (a+b)(a−b)−8a =4a−4b−8a =−4a−4b =−4(a+b) =−4(4) =−16
$${a}+{b}={b}+{c}\Rightarrow{a}={c} \\ $$$$\left({a}+{b}\right)\left({a}−{b}\right)−\mathrm{8}{a} \\ $$$$=\mathrm{4}{a}−\mathrm{4}{b}−\mathrm{8}{a} \\ $$$$=−\mathrm{4}{a}−\mathrm{4}{b} \\ $$$$=−\mathrm{4}\left({a}+{b}\right) \\ $$$$=−\mathrm{4}\left(\mathrm{4}\right) \\ $$$$=−\mathrm{16} \\ $$
Answered by Rasheed.Sindhi last updated on 03/Mar/25
If a+b=b+c=4 find: a^2 −b^2 −8c = ? •a+b=b+c=4 ⇒a=c=4−b •a^2 −b^2 −8c =(4−b)^2 −b^2 −8(4−b) =16+b^2 −8b−b^2 −32+8b =−16
$$\mathrm{If}\:\:\:\mathrm{a}+\mathrm{b}=\mathrm{b}+\mathrm{c}=\mathrm{4} \\ $$$$\mathrm{find}:\:\:\:\mathrm{a}^{\mathrm{2}} −\mathrm{b}^{\mathrm{2}} −\mathrm{8c}\:=\:? \\ $$$$\bullet\mathrm{a}+\mathrm{b}=\mathrm{b}+\mathrm{c}=\mathrm{4} \\ $$$$\:\:\Rightarrow\mathrm{a}=\mathrm{c}=\mathrm{4}−\mathrm{b} \\ $$$$\:\bullet\mathrm{a}^{\mathrm{2}} −\mathrm{b}^{\mathrm{2}} −\mathrm{8c}\: \\ $$$$\:\:\:\:=\left(\mathrm{4}−\mathrm{b}\right)^{\mathrm{2}} −\mathrm{b}^{\mathrm{2}} −\mathrm{8}\left(\mathrm{4}−\mathrm{b}\right) \\ $$$$\:\:\:\:=\mathrm{16}+\cancel{\mathrm{b}^{\mathrm{2}} }−\cancel{\mathrm{8b}}−\cancel{\mathrm{b}^{\mathrm{2}} }−\mathrm{32}+\cancel{\mathrm{8b}} \\ $$$$\:\:\:\:=−\mathrm{16} \\ $$

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