Question
Write the cube in expanded form: ${\left( {2x + 1} \right)^3}$
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Answer
${\left( {2x + 1} \right)^3}$
We know that ${\left( {a + b} \right)^3} = {a^3} + {b^3} + 3ab\left( {a + b} \right)$
$\therefore {\left( {2x + 1} \right)^3} = {\left( {2x} \right)^3} + {\left( 1 \right)^3} + 3 \times 2x \times 1\left( {2x + 1} \right)$
$ = 8{x^3} + 1 + 6x\left( {2x + 1} \right)\,$
$= 8{x^3} + 12{x^2} + 6x + 1.$
Therefore, the expansion of the expression ${\left( {2x + 1} \right)^3}$ is $8{x^3} + 12{x^2} + 6x + 1$
We know that ${\left( {a + b} \right)^3} = {a^3} + {b^3} + 3ab\left( {a + b} \right)$
$\therefore {\left( {2x + 1} \right)^3} = {\left( {2x} \right)^3} + {\left( 1 \right)^3} + 3 \times 2x \times 1\left( {2x + 1} \right)$
$ = 8{x^3} + 1 + 6x\left( {2x + 1} \right)\,$
$= 8{x^3} + 12{x^2} + 6x + 1.$
Therefore, the expansion of the expression ${\left( {2x + 1} \right)^3}$ is $8{x^3} + 12{x^2} + 6x + 1$
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