Question

factorise 125k3+27m3​

Answer 1

$\underline{\textbf{Given:}}$

$\mathsf{125\,k^3+27\,m^3}$

$\underline{\textbf{To find:}}$

$\textsf{Factors of}$

$\mathsf{125\,k^3+27\,m^3}$

$\underline{\textbf{Solution:}}$

$\underline{\textbf{Formula used:}}$

$\;\;\;\boxed{\mathsf{a^3+b^3=(a+b)(a^2-ab+b^2)}}$

$\mathsf{Consider,}$

$\mathsf{125\,k^3+27\,m^3}$

$\mathsf{=(5k)^3+(3m)^3}$

$\textsf{Using the above algebraic formula, we get}$

$\mathsf{=(5k+3m)\,((5k)^2-(5k)(3m)+(3m)^2)}$

$\mathsf{=(5k+3m)\,(25k^2-15km+9m^2)}$

$\implies\boxed{\mathsf{125\,k^3+27\,m^3=(5k+3m)\,(25k^2-15km+9m^2)}}$

$\underline{\textbf{Find more:}}$

Factorise x^3-y^3  

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Answer 2

factorise 125k3+ 27m3.