Find the values of following polynomials at m = 1, n = -1 and p = 2(a)

1.	Find the values of following polynomials at m = 1, n = -1 and p = 2(a) m+n+p(b) m2+n2+P2(c) m3+ n3+p3(d) mn+np + pm(e) m3 +n3 + p3 -3mnp(f) m2n2 +n2p2 +p2m2
Answer» Given, m = 1, n = -1 and p = 2 So, putting m = 1, n = -1 and p = 2 in the given expressions, we get (a) m+n+p = 1-1+2 = 2 (b) m²+n²+P² =(1)² + (-1)² + (2)² =1+1+ 4 = 6 (c) m³+ n³+p³ =(1)³ + (-1)³ + (2)³ = 1 -1 + 8 = 8 (d) mn+np+ pm = (1)(-1)+(-1)(2)+(2)(1) = -1-2 + 2 = -1 (e) m³ +n³ + p³ -3mnp = (1)³ + (-1)³ + (2)³ -3(1)(-1)(2) = 1-1+8+6 = 14 (f) m²n² +n²p² +p²m² = (1)² (-1)² + (-1)² (2)² + (2)² (1)² = 1+ 4+ 4 = 9

Find the values of following polynomials at m = 1, n = -1 and p = 2(a) m+n+p(b) m2+n2+P2(c) m3+ n3+p3(d) mn+np + pm(e) m3 +n3 + p3 -3mnp(f) m2n2 +n2p2 +p2m2

Answer»

Given, m = 1, n = -1 and p = 2

So, putting m = 1, n = -1 and p = 2 in the given expressions, we get

(a) m+n+p

= 1-1+2

= 2
(b) m²+n²+P²

=(1)² + (-1)² + (2)²

=1+1+ 4

= 6
(c) m³+ n³+p³

=(1)³ + (-1)³ + (2)³

= 1 -1 + 8

= 8
(d) mn+np+ pm

= (1)(-1)+(-1)(2)+(2)(1)

= -1-2 + 2

= -1
(e) m³ +n³ + p³ -3mnp

= (1)³ + (-1)³ + (2)³ -3(1)(-1)(2)

= 1-1+8+6

= 14
(f) m²n² +n²p² +p²m²

= (1)² (-1)² + (-1)² (2)² + (2)² (1)²

= 1+ 4+ 4

= 9