Question

Write the following cubes in expanded form :-
${(2x + 1)}^{3}$
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Answer 1

ANSWER :-

We have to expand ${(2x + 1)}^{3}$

For this problem, we must know the given formula below -

${(a + b)}^{3} = \: {a}^{3} + {b}^{3} + 3ab(a + b)$

$Now, \\ \\ {(2x + 1)}^{3} = ( {2x)}^{3} + {(1)}^{3} + 3(2x)(1)(2x + 1) \\ \\ = > {(2x + 1)}^{3} = 8 {x}^{3} + 1 + 6x(2x + 1) \\ \\ = > {(2x + 1)}^{3} = 8 {x}^{3} +1 + 12 {x}^{2} + 6x$

Hence, the expanded form of ${(2x + 1)}^{3}$ is $8 {x}^{3} +1 + 12 {x}^{2} + 6x$

Answer 2

$\rightarrow \sf \red{( {2x + 1)}^{3} } \\ \rightarrow \sf{ {(2x)}^{3} + {(1)}^{3} + 3 \times 2x \times 1(2x + 1) } \\ \rightarrow \sf{ {8x}^{3} + 1 + 6x(2x + 1) } \\ \rightarrow \sf{ {8x}^{3} + 1 + {12x}^{2} + 6x}$

$\bullet \bf \red{ \: formula \rightarrow} \sf { {a}^{3} + {b}^{3} + 3ab(a + b) }$