Write the following cubes in the expanded form $(2 p - 5)^{3}$

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Solution

We know that $(x + y)^{3} = x^{3} + y^{3} + 3 x y (x + y)$
$(2 p - 5)^{3}$
Here x=2p and y=-5 we get
$(2 p)^{3} - (5)^{3} + 3 (2 p) (- 5) (2 p - 5)$
= $8 p^{3} - 125 - 30 p (2 p - 5)$
= $8 p^{3} - 125 - 60 p^{2} + 150 p$
= $8 p^{3} - 60 p^{2} + 150 p - 125$

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