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

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Solution

${(2 x + 1)}^{3}$

Using identity ${(x + y)}^{3}$ = $x^{3}$ + $y^{3}$ + 3xy(x + y)

= ${(2 x)}^{3}$ + ${(1)}^{3}$ + 3(2x)(1)(2x + 1)

= 8 $x^{3}$ + 1 + 6x(2x + 1)

= 8 $x^{3}$ + 1 + 12 $x^{2}$ + 6x

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