Maharashtra Board Solutions for Exercise 2: Practice Set 6.2

Factorising $x^{3 }+ 64y^3$ gives $\left(x+4y\right)\left(x^2-4xy+k{y}^2\right)$. Find the value of $k$.

Factorising $125p^{3 }+ q^3$ gives $\left(5\mathrm{p}+\mathrm{q}\right)\left({\mathrm{kp}}^2-5\mathrm{pq}+{\mathrm{q}}^2\right)$. Find the value of $\mathrm{k}$.

Factorising $125{\mathrm{k}}^3 + 27{\mathrm{m}}^3$ gives$\left(5\mathrm{k}+3\mathrm{m}\right)\left({\mathrm{ak}}^2-15\mathrm{km}+9{\mathrm{m}}^2\right)$. Find the value of $\mathrm{a}$.

Factorisation of $2l^{3 }+ 432m3$ is $k\left(l+6m\right)\left(l^2-6ml+36m^2\right)$. Find the value of $k$.

Factorisation of $24a^3 + 81b^3$ is $k\left(2a+3b\right)\left(4a^2-6ab+9b^2\right)$. Find the value of $k$.

Factorisation of  $y^3+\frac{1}{8y^3}$ is $\left(y+\frac{1}{ky}\right)\left(y^2-\frac{1}{2}+\frac{1}{4y^2}\right)$. Find the value of $k$.

Factorisation of $a^3+\frac{8}{a^3}$is $\left(a+\frac{k}{a}\right)\left(a^2-2+\frac{4}{a^2}\right)$. Find the value of $k$.

Factorisation of $1+\frac{q^3}{125}$ is $\left(1+\frac{q}{k}\right)\left(1-\frac{q}{5}+\frac{q^2}{25}\right)$.