If $m = 1, n = 2, p = - 3$ find the value of $m^{4} n + n^{4} m + m n p - p^{3}$

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Solution

$= m^{4} n + n^{4} m + m n p - p^{3} = {(1)}^{4} (2) + {(2)}^{4} (1) + (1 \times 2 \times - 3) - {(- 3)}^{3} = 2 + 16 + (- 6) - (- 27) = 18 - 6 + 27 = 39$

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Question 67 (e)

Find the value of the given polynomial at m = 1, n = -1 and p = 2

$m^{3} + n^{3} + p^{3} - 3 m n p .$

Simplify :

1. $\frac{16 m^{3} y^{2}}{4 m^{2} y}$

2. $\frac{32 m^{2} n^{3} p^{2}}{4 m n p}$

If in an A.P., $S_{n} = n^{2} p$ and $S_{m} = m^{2} p$ , where $S_{r}$ denotes the sum of r terms of the A.P., then $S_{p}$ is equal to

If the coefficient of $m^{t h}$ , $(m + 1)^{t h}$ and $(m + 2)^{t h}$ terms in the expansion of $(1 + x)^{n}$ are in A.P., then:

m^{3} + n^{3} + p^{3} - 3 m n p

m = 1

n = - 1

p = 2

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