Algebraic Identities

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

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

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

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

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

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

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

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: $27{\mathrm{p}}^3-\frac{1}{216}-\frac{9}{2}{\mathrm{p}}^2+\frac{1}{4}\mathrm{p}$.

Factorise the following: $64a^3-27b^3-144a^{2}b+108a{b}^2$

Factorise the following: $27-125a^3-135a+225a^2$.

Factorise the following: $8{\mathrm{a}}^3-{\mathrm{b}}^3-12{\mathrm{a}}^2\mathrm{b}+6\mathrm{a}{\mathrm{b}}^2$.
 

Evaluate using suitable identities: ${\left(99\right)}^3$.
 

Evaluate the following using suitable identities: ${\left(102\right)}^3$

Evaluate the following using suitable identities: ${\left(998\right)}^3$.

The expanded form of the cube ${\left(\mathrm{x}-\frac{2}{3}\mathrm{y}\right)}^3$ is ${\mathrm{x}}^3-k {\mathrm{x}}^2\mathrm{y}+\frac{4}{3}{\mathrm{xy}}^2-\frac{8\mathrm{x}}{27}{\mathrm{y}}^3$. Find the value of $k$.

The expanded form of the cube ${\left(\frac{3}{2}\mathrm{x}+1\right)}^3$ is $\frac{27}{8}{\mathrm{x}}^3+\frac{k {\mathrm{x}}^2}{4}+\frac{9\mathrm{x}}{2}+1$. Find the value of $k$.

The expanded form of the cube ${\left(2\mathrm{a}-3\mathrm{b}\right)}^3$ is $8{\mathrm{a}}^3-36{\mathrm{a}}^2\mathrm{b}+k {\mathrm{ab}}^2-27{\mathrm{b}}^3$. Find the value of $k$.

The expanded form of the cube ${(2x+1)}^3$ is $8{\mathrm{x}}^3+k {\mathrm{x}}^2+6\mathrm{x}+1$. Find the value of $k$.

Factorise: $2x^2+y^2+8z^2-2\sqrt{2}xy+4\sqrt{2}yz-8xz$