Factorization

$a^3+b^3=(a+b)(a^2+b^2-ab)$ Here we know the value of $a+b$ ,we just have to find the value of $a^2+b^2,ab$ .First let,s find $ab$ : $a^2b+ab^2=ab(a+b)=ab\times15=810\rightarrow ab=\frac{810}{15}=54$ So $ab=54$ .Now let,s find $a^2+b^2$ : $(a+b)^2=15^2\rightarrow a^2+b^2+2ab=225$ $a^2+b^2+2(54)=225\rightarrow a^2+b^2=225-108=117$ Now we have found the necessary data.Let,s calculate $a^3+b^3$ : $(a+b)(a^2+b^2-ab)\rightarrow 15\times(117-54)=15\times63=\boxed{945}$

$(a+b)^{3}=a^{3}+3a^{2}b+3ab^{2}+b^{3}$ . But we know $(a+b)^{3}=15^{3}=3375$ . And we know that $3a^{2}b+3ab^{2}=3(a^{2}b+ab^{2})=3(810)=2430$ . Therefore, $3375=a^{3}+b^{3}+2430$ , and $a^{3}+b^{3}=3375-2430=975$ .

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