Let us factorize the following algebraic expressions:

AR³ – Ar³ + AR²h – Ar²h

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)