# Let us factorize

Given,

AR3 – Ar3 + AR2h – Ar2h

= A(R3 – r3 + R2h – r2h)

= A[(R3 – r3) + h(R2 – r2)]

We know, a3 – b3 = (a – b)(a2 + ab + b2) and a2 – b2 = (a + b)(a – b)

= A [(R – r) ( R2 + Rr + r2) + h (R + r)(R – r)]

= A(R – r) [R2 + Rr + r2 + h (R + r)]

= A(R – r) [R(R + r) + r2 + h(R + r)]

= A(R – r) (R + r) (R + r2 + h)

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