Find (a + b)⁴ - (a - b)⁴. Hence, evaluate \({ \left( \sqrt { 3 } +\sqrt { 2 } \right) }^{ 4 }-{ \left( \sqrt { 3 } -\sqrt { 2 } \right) }^{ 4 }\)

Find the middle term(s) in the given expansion.
\(\left( \frac { x }{ 3 } +9y \right) ^{ 10 }\)

Find the coefficient of xⁿ in the expansion of (1+x)ⁿ (1-x)ⁿ

Expand the following expansions.
(1-x²)^7/3

Using binomial theorem, expand the following expressions.
\(\left( x-\frac { 1 }{ 2x } \right) ^{ 5 }\)

Using binomial theorem, expand the following expansions.
\(\left( { x }^{ 2 }+3+2\sqrt { 3x } \right) ^{ 3 }\)

Find the number of terms in the expansions of following expressions.
(1-z)⁴

Evaluate the following terms. 6th term in the expansion of \(\left( y-\frac { 1 }{ y } \right) ^{ 20 }.\)

Compute the value of \(\left( 96 \right) ^{ 3 }\)

Find the number of terms in the expansions of the following expressions.
\(\left( 1+\sqrt { 5x } \right) ^{ 7 }+\left( 1-\sqrt { 5x } \right) ^{ 7 }\)

Evaluate \(\sqrt [ 3 ]{ 126 } \) correct to 5 decimal places.

Find the equation of hyperbola, if vertices are at \(\left( \pm 7,0 \right) \) and e=4/3.

For what value of m, the coefficients of the (2m + 1)th and (4m + 5)th terms in the expansion of (1 + x)¹⁰ are equal?

Find the two successive terms in the expansion of (1+x)²⁴, whose coefficients are in the ratio 1:4

Find the greatest value of term independent of x in the expansion of  \(\left( x\quad sin\alpha +\frac { cos\alpha }{ x } \right) ^{ 10 }\) ,where \(\alpha \varepsilon R\)

Prove that 11ⁿ-10n, when divided by 100, always leave a remainder 1 where n\(\in\)+N