EXERCISE

Use suitable identity, find the product of $\left(y^2+\frac{3}{2}\right)\left(y^2-\frac{3}{2}\right)$.

Expand, using suitable Identities: ${\left(-2\mathrm{x}+5\mathrm{y}-3\mathrm{z}\right)}^2$.

Verify: ${\mathrm{x}}^3-{\mathrm{y}}^3=\left(\mathrm{x}-\mathrm{y}\right)\left({\mathrm{x}}^2+\mathrm{x}\mathrm{y}+{\mathrm{y}}^2\right)$.

Factorise the following: $64{\mathrm{m}}^3-343{\mathrm{n}}^3$.

Without actually calculating the cubes, find the value of the following: ${\left(-12\right)}^3+{\left(7\right)}^3+{\left(5\right)}^3$.
 

Without actually calculating the cubes, find the value of the following: ${\left(28\right)}^3+{\left(-15\right)}^3+{\left(-13\right)}^3$.

Give possible expressions for the length and breadth of the following rectangle, in which the area is given: $35{\mathrm{y}}^2+13\mathrm{y}-12$.

What are the possible expressions for the dimension of the cuboids whose volume is given below?

Volume $=12\mathrm{k}{\mathrm{y}}^2+8\mathrm{k}\mathrm{y}-20\mathrm{k}$.