By using formula; a^3 b^3 = ( a b)( a^2 + ab + b^2) we have, [ =( 2x 3 ( 2x 3 ) #160; ) ( ( 2x+3 ) #160; ^ 2 +( 2x+3 ) ( 2x 3 ) +( 2x 3 ) ...

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Algebraic Identities

Solve: 2x+33...

Question

Solve:
$(2 x + 3)^{3} - (2 x - 3)^{3}$

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Solution

By using formula;- $a^{3} - b^{3} = (a - b) (a^{2} + a b + b^{2})$
we have,
$\begin{matrix} = (2 x - 3 - (2 x - 3)) ({(2 x + 3)}^{2} + (2 x + 3) (2 x - 3) + {(2 x - 3)}^{2}) = (2 x - 3 - 2 x + 3) (4 x + 9 + 12 x + 4 x^{2} - 6 x + 6 x - 9 + 4 x + 9 - 12 x) = 4 x^{2} + 8 x + 9 \end{matrix}$
on simplifying we get, $(4 x^{2} + 8 x + 9)$

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