Expand the following identity.
${(2 x + 1)}^{3}$

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

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

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

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

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Solution

The correct option is D
${8 x}^{3} + 1 + 12 x^{2} + 6 x$

We know that ${(x + y)}^{3}$ = $x^{3} + y^{3} + 3 x y (x + y)$
= $x^{3} + y^{3} + 3 x^{2} y + 3 x y^{2}$ -----(i)

Comparing the question with the identity, we have x = 2x, y = 1

Substitute the value of x and y in (i), we get:

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

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

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