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Mathematics
Algebraic identities
Expand the following using identities: ${\left( {3x - 4y} \right)^2}$.

Mathematics
Algebraic identities
Expand the following: $${\left( {3a + 2b} \right)^3}$$.
A.$$27{a^3} + 54{a^2}b + 6a{b^2} + 8{b^3}$$
B.$$27{a^3} + 54{a^2}b + 36a{b^2} + 8{b^3}$$
C.$$27{a^3} + 54{a^2}b + 36a{b^2} + 2{b^3}$$
D.$$9{a^3} + 54{a^2}b + 36a{b^2} + 8{b^3}$$

Mathematics
Algebraic identities
Find the values of \[\dfrac{{{\left( \sqrt{\sqrt{3}+1}+\sqrt{\sqrt{3}-1} \right)}^{2}}\left( \sqrt{3}-\sqrt{2} \right)}{{{\left( \sqrt{\sqrt{3}+1} \right)}^{2}}-{{\left( \sqrt{\sqrt{3}-1} \right)}^{2}}}\]
1. \[\dfrac{\sqrt{3}+\sqrt{2}}{\sqrt{3}}\]
2. \[1\]
3. \[\sqrt{3}\]
4. \[\dfrac{1}{\sqrt{3}}\]
Mathematics
Algebraic identities
Evaluate ${\left( {102} \right)^3}$ using the appropriate identities.
Mathematics
Algebraic identities
Find the following product by using suitable properties $1938 \times 99$
Mathematics
Algebraic identities
Evaluate \[\sqrt[3]{121}\times \sqrt[3]{297}\]
Mathematics
Algebraic identities
What is a square plus b square?

Mathematics
Algebraic identities
The difference of the squares \[\left( {{61}^{2}}-{{51}^{2}} \right)\] is equal to?
Mathematics
Algebraic identities
If $ a + b = 9 $ , $ ab = 4 $ , find the value of $ {a^2} + {b^2} $
Mathematics
Algebraic identities
Use identities to evaluate \[{\left( {97} \right)^2}\] .
Mathematics
Algebraic identities
Find the value of \[{513^2} - {512^2}\]
Mathematics
Algebraic identities
Find the value of $x$, if $4x=\left(52\right)^2-\left(48\right)^2$.
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