Question
Write $(5 p-3 q)^3$ in the expanded form.
✓
Answer
Comparing the given expression with $(x-y)^3$,
we find that $x=5 p, y=3 q$.
So, using Identity $(x-y)^3=x^3-3 x^2 y+3 x y^2-y^3$,
we have: $(5 p-3 q)^3=(5 p)^3-(3 q)^3-3(5 p)(3 q)(5 p-3 q)$
$=125 p^3-27 q^3-225 p^2 q+135 p q^2$
This is the required expansion.
we find that $x=5 p, y=3 q$.
So, using Identity $(x-y)^3=x^3-3 x^2 y+3 x y^2-y^3$,
we have: $(5 p-3 q)^3=(5 p)^3-(3 q)^3-3(5 p)(3 q)(5 p-3 q)$
$=125 p^3-27 q^3-225 p^2 q+135 p q^2$
This is the required expansion.
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