Applications of Identities

If $\mathrm{x}-\frac{1}{\mathrm{x} }=\frac{3}{2}$ then find the value of ${\mathrm{x}}^2+\frac{1}{{\mathrm{x}}^2 }$ :

If $\mathrm{x}+\frac{1}{\mathrm{x} }=\frac{10}{3}$ then find the value of ${\mathrm{x}}^2+\frac{1}{{\mathrm{x}}^2 }$?

Simplify the following : $\mathrm{x}(2\mathrm{y}-3\mathrm{z})+\mathrm{y}(3\mathrm{z}-2\mathrm{x})+3\mathrm{z}(\mathrm{x}-\mathrm{y})$

Simplify the following : $\mathrm{a}(\mathrm{b}-\mathrm{c})+\mathrm{b}(\mathrm{c}-\mathrm{a})+\mathrm{c}(\mathrm{a}-\mathrm{b})$

Using identities find the value of the following: $501\times 502$

Using identities find the value of the following: $95\times 103$

Using identities find the value of the following: 

$78\times 82$

If $a-\frac{1}{a}=0$ , then find the value of $a^2+\frac{1}{a^2}$

If $a+\frac{1}{a}=\frac{5}{2}$ , then find the value of $a^2+\frac{1}{a^2}$

Using identities evaluate.

$10.5\times 9.5$

Using identities evaluate:

$52\times 48$

Using identities find the value of the following:

$103\times 97$

Find the value of the following using the identity : $(9.8{)}^2$

Find the value of the following using the identity : $(10.2{)}^2$

Find the value of the following using the identity : ${997}^2$

Find the value of the following using the identity : ${95}^2$

Find the value of the following using the identity : ${98}^2$

Find the value of the following using the identity : ${49}^2$

Find the value of the following using the identity : ${1001}^2$

Find the value of the following using the identity : ${302}^2$