Q.1 Identify the terms, their coefficients for each of the following expressions.
(i) (ii)
(iii)
(iv) (v)
(vi)
Sol. (i)
Terms: and
Coefficients: 5 in and -3 in
(ii)
Terms:,
and
Coefficients: 1 in 1, 1 in and 1 in
(iii)
Terms:,
and
Coefficients: 4 in, - 4 in
and 1 in
(iv)
Terms: ,
,
and
Coefficients: 3 in 3. -1 in , 1 in
and -1 in
(v)
Terms: ,
and
Coefficients: in
,
in
and -1 in
(vi)
Terms:,
and
Coefficients: 0.3 in , -0.6 in
and 0.5 in
Q.2 Classify the following polynomials as monomials, binomials, trinomials. Which polynomials do not fit in any of these three categories?
,
,
,
,
,
,
,
,
,
,
Sol. The classification of polynomials as monomials, binomials, trinomials are as follows:
Monomials:
Binomials:
Trinomials:
Polynomials that do not fit in any of these categories:
Q.3 Add the following.
(i)
(ii)
(iii)
(iv)
Sol. (i)
& {\rm{ }}ab{\rm{ }} - {\rm{ }}bc \cr
& + {\rm{ }}bc{\rm{ }} - {\rm{ }}ca \cr
& + {\rm{ }} - {\rm{ }}ab{\rm{ }} + {\rm{ }}ca \cr} " />
Hence, addition of is 0.
(ii)
& {\rm{ }}a{\rm{ }} - {\rm{ }}b{\rm{ }} + {\rm{ }}ab \cr
& + {\rm{ }}b{\rm{ }} - {\rm{ }}c{\rm{ }} + {\rm{ }}bc \cr
& + {\rm{ }} - {\rm{ }}a{\rm{ }} + {\rm{ }}c{\rm{ }} + {\rm{ }}ac \cr} " />
Hence, addition of is ab + bc + ac.
(iii)
& {\rm{ }}2{p^2}{q^2} - {\rm{ }}3pq{\rm{ }} + {\rm{ }}4 \cr
& + {\rm{ }} - 3{p^2}{q^2} + 7pq{\rm{ }} + {\rm{ }}5 \cr} " />
Hence, addition of is
.
(iv)
& {\rm{ }}{l^2} + {m^2} \cr
& + {\rm{ }}{m^2} + {n^2} \cr
& + {\rm{ }}{l^2}{\rm{ }} + {n^2} \cr
& + {\rm{ }}2lm + 2mn + 2nl \cr} " />
Hence, addition ofis
Q.4 . (a) Subtract from
(b) Subtract from
(c) Subtract from
Sol.
(a)
& {\rm{ }}12a{\rm{ }} - {\rm{ }}9ab{\rm{ }} + {\rm{ }}5b{\rm{ }} - {\rm{ }}3 \cr
& {\rm{ }}4a{\rm{ }} - {\rm{ }}7ab{\rm{ }} + {\rm{ }}3b{\rm{ }} + 12 \cr
& ( - ){\rm{ }}( + ){\rm{ }}( - ){\rm{ }}( - ) \cr} " />
(b)
& {\rm{ }}5xy - {\rm{2yz}} - {\rm{2zx + 10xyz}} \cr
& {\rm{ 3xy + 5yz}} - {\rm{7zx}} \cr
& ( - ){\rm{ }}( - ){\rm{ }}( + ){\rm{ }} \cr} " />
(c)
& {\rm{ }}18 - 3p - 11q + 5pq - 2p{q^2} + 5{p^2}q{\rm{ }} \cr
& - {\rm{ }}10 - 8p + 7q - 3pq + 5p{q^2} + 4{p^2}q \cr
& ( + )( + ){\rm{ }}( - ){\rm{ }}( + ){\rm{ }}( - ){\rm{ }}( - ){\rm{ }} \cr} " />