Write the following cube in expanded form: $(2x + 7)^3$.
To expand the expression $(2x + 7)^3$,we use the algebraic identity: $(a + b)^3 = a^3 + b^3 + 3a^2b + 3ab^2$.
Here,$a = 2x$ and $b = 7$.
Substituting these values into the identity:
$(2x + 7)^3 = (2x)^3 + (7)^3 + 3(2x)^2(7) + 3(2x)(7)^2$
$= 8x^3 + 343 + 3(4x^2)(7) + 3(2x)(49)$
$= 8x^3 + 343 + 84x^2 + 294x$
Rearranging the terms in descending order of powers:
$= 8x^3 + 84x^2 + 294x + 343$.
Here,$a = 2x$ and $b = 7$.
Substituting these values into the identity:
$(2x + 7)^3 = (2x)^3 + (7)^3 + 3(2x)^2(7) + 3(2x)(7)^2$
$= 8x^3 + 343 + 3(4x^2)(7) + 3(2x)(49)$
$= 8x^3 + 343 + 84x^2 + 294x$
Rearranging the terms in descending order of powers:
$= 8x^3 + 84x^2 + 294x + 343$.
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