Write the following cube in expanded form: $(2x + 1)^3$
(A) To expand $(2x + 1)^3$,we use the algebraic identity: $(a + b)^3 = a^3 + b^3 + 3ab(a + b)$.
Here,$a = 2x$ and $b = 1$.
Substituting these values into the identity:
$(2x + 1)^3 = (2x)^3 + (1)^3 + 3(2x)(1)(2x + 1)$
Calculating the terms:
$= 8x^3 + 1 + 6x(2x + 1)$
Distributing $6x$ into the parentheses:
$= 8x^3 + 1 + 12x^2 + 6x$
Rearranging in descending order of powers:
$= 8x^3 + 12x^2 + 6x + 1$
Here,$a = 2x$ and $b = 1$.
Substituting these values into the identity:
$(2x + 1)^3 = (2x)^3 + (1)^3 + 3(2x)(1)(2x + 1)$
Calculating the terms:
$= 8x^3 + 1 + 6x(2x + 1)$
Distributing $6x$ into the parentheses:
$= 8x^3 + 1 + 12x^2 + 6x$
Rearranging in descending order of powers:
$= 8x^3 + 12x^2 + 6x + 1$
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