Write the following cube in expanded form:
$(2a - 5b)^3$
$(2a - 5b)^3$
(N/A) To expand the expression $(2a - 5b)^3$,we use the algebraic identity:
$(x - y)^3 = x^3 - y^3 - 3xy(x - y)$
Here,$x = 2a$ and $y = 5b$.
Substituting these values into the identity:
$= (2a)^3 - (5b)^3 - 3(2a)(5b)(2a - 5b)$
$= 8a^3 - 125b^3 - 30ab(2a - 5b)$
$= 8a^3 - 125b^3 - 60a^2b + 150ab^2$
$(x - y)^3 = x^3 - y^3 - 3xy(x - y)$
Here,$x = 2a$ and $y = 5b$.
Substituting these values into the identity:
$= (2a)^3 - (5b)^3 - 3(2a)(5b)(2a - 5b)$
$= 8a^3 - 125b^3 - 30ab(2a - 5b)$
$= 8a^3 - 125b^3 - 60a^2b + 150ab^2$
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