Question

plzzzz solve it..... ​

Answer 1

Answer:-

$\left(m^2+9\right)^2$

Step-by-step explanation:

$m^4+18m^2+81$

$\gray{\mathrm{Let\:}M=m^2}$

$=M^2+18M+81$

$\mathrm{Factorise}\:M^2+18M+81:$

$\gray{\mathrm{Break\:the\:expression\:into\:groups}}$

$=\left(M^2+9M\right)+\left(9M+81\right)$

$\gray{\mathrm{Factor\:out\:}M\mathrm{\:from\:}M^2+9M\mathrm{:\quad }M\left(M+9\right)}$

$\gray{\mathrm{Factor\:out\:}9\mathrm{\:from\:}9M+81\mathrm{:\quad }9\left(M+9\right)}$

$=M\left(M+9\right)+9\left(M+9\right)$

$\gray{\mathrm{Factor\:out\:common\:term\:}u+9}$

$=\left(M+9\right)\left(M+9\right)$

$\gray{\mathrm{Substitute\:back}\:M=m^2}$

$=\left(m^2+9\right)\left(m^2+9\right)$

$\gray{\mathrm{Simplify}}$

$=\left(m^2+9\right)^2$

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Answer 2

Answer:

Answer:-

$\left(m^2+9\right)^2$

Step-by-step explanation:

$m^4+18m^2+81$

$\gray{\mathrm{Let\:}M=m^2}$

$=M^2+18M+81$

$\mathrm{Factorise}\:M^2+18M+81:$

$\gray{\mathrm{Break\:the\:expression\:into\:groups}}$

$=\left(M^2+9M\right)+\left(9M+81\right)$

$\gray{\mathrm{Factor\:out\:}M\mathrm{\:from\:}M^2+9M\mathrm{:\quad }M\left(M+9\right)}$

$\gray{\mathrm{Factor\:out\:}9\mathrm{\:from\:}9M+81\mathrm{:\quad }9\left(M+9\right)}$

$=M\left(M+9\right)+9\left(M+9\right)$

$\gray{\mathrm{Factor\:out\:common\:term\:}u+9}$

$=\left(M+9\right)\left(M+9\right)$

$\gray{\mathrm{Substitute\:back}\:M=m^2}$

$=\left(m^2+9\right)\left(m^2+9\right)$

$\gray{\mathrm{Simplify}}$

$=\left(m^2+9\right)^2$

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