Write the following cube in expanded form: $(3a + 5b)^3$.
(N/A) To expand $(3a + 5b)^3$,we use the algebraic identity $(x + y)^3 = x^3 + y^3 + 3xy(x + y)$.
Here,$x = 3a$ and $y = 5b$.
Substituting these values into the identity:
$(3a + 5b)^3 = (3a)^3 + (5b)^3 + 3(3a)(5b)(3a + 5b)$
$= 27a^3 + 125b^3 + 45ab(3a + 5b)$
$= 27a^3 + 125b^3 + 135a^2b + 225ab^2$.
Here,$x = 3a$ and $y = 5b$.
Substituting these values into the identity:
$(3a + 5b)^3 = (3a)^3 + (5b)^3 + 3(3a)(5b)(3a + 5b)$
$= 27a^3 + 125b^3 + 45ab(3a + 5b)$
$= 27a^3 + 125b^3 + 135a^2b + 225ab^2$.
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