8th Maths 9.1
Chapter 9
Algebraic Expressions and Identities
NCERT Class 8th solution of Exercise 9.2
NCERT Class 8th solution of Exercise 9.3
NCERT Class 8th solution of Exercise 9.4
NCERT Class 8th solution of Exercise 9.5
Exercise 9.1
Q1. Identify the terms, their coefficients for each of the following expressions.
i) `5xyz^2 - 3zy,`
ii) `1 + x + x^2,`
iii) `4x^2y^2 - 4x^2y^2z^2 + z^2,`
iv) `3 - pq + qr - rp,`
v) `x/2 + y/2 - xy,`
vi) `0.3a - 0.6ab + 0.5b,`
`text{Answer:}`
Q2. Classify the following polynomials as monomials, binomials, trinomials. Which polynomials do not fit in any of these three categories?
`x+y`
`1000`
`x + x^2 + x^3 + x^4,`
`7 + y + 5x`,
`2y - 3y^2`,
`2y - 3y^2 + 4y^3`,
`5x - 4y + 3xy,`
`4z - 15z^2,`
`ab + bc + cd + da,`
`pqr`,
`p^2r + pq^2,`
`2p + 2q,`
`text{Answer:}`
Q3. Add the following.
i) `ab - bc, bc - ca, ca - ab,`
ii) `a - b + ab, b - c + bc, c - a + ac`,
iii) `2p^2q^2 - 3pq + 4, 5 + 7pq - 3p^2q^2`,
iv) `l^2 + m^2, m^2 + n^2, n^2 + l^2, 2lm + 2mn + 2nl`
`text{Sol.}`
i) `ab - bc + bc - ca + ca - ab`
`text{Rearrange the like terms}`
`= ab - ab + bc + bc - ca + ca`
`= 0`
`text{Answer:}`
`0`
ii) `a - b + ab + b - c + bc + c - a + ac`
`text{Rearrange the like terms}`
`= a - a + b - b + c - c + ab + bc + ac`
`= ab + bc + ac`
`text{Answer:}`
`ab + bc + ac`
iii) `2p^2q^2 - 3pq + 4 + 5 + 7pq - 3p^2q^2`
`text{Rearrange the like terms}`
`= 2p^2q^2 - 3p^2q^2 - 3pq + 7pq + 9`
`= - p^2q^2 + 4pq + 9`
`text{Answer:}`
`-p^2q^2 + 4pq + 9`
iv) `l^2 + m^2 + m^2 + n^2 + n^2 + l^2 + 2lm + 2mn`` + 2nl`
`text{Rearrange the like terms}`
`= l^2 + l^2 + m^2 + m^2 + n^2 + n^2 + 2lm + 2nm`` + 2nl`
`= 2l^2 + 2m^2 + 2n^2 + 2lm + 2nm + 2nl`
`= 2(l^2 + m^2 + n^2 + lm + nm + nl)`
`text{Answer:}`
`2(l^2 + m^2 + n^2 + lm + nm + nl)`
Q4.
a) Subtract `4a - 7ab + 3b + 12 text{ from}`` 12a -9ab + 5b - 3`
b) Subtract `3xy + 5yz - 7zx text{ from}`` 5xy - 2yz - 2zx + 10xyz`
c) Subtract `4p^2q - 3pq + 5pq^2 - 8p - 7q - 10 text{ from}`` 18 - 3p - 11q + 5pq - 2pq^2 + 5p^2q`
`text{Sol.}`
a) `12a - 9ab + 5b - 3 - (4a - 7ab + 3b + 12)`
`= 12a - 9ab + 5b - 3 - 4a + 7ab - 3b - 12`
`text{Rearrange the like terms}`
`= 12a - 4a + 5b - 3b + 7ab - 9ab - 3 - 12`
`= 8a + 2b - 2ab - 15`
`text{Answer:}`
`= 8a - 2ab + 2b - 15`
b) `5xy - 2yz - 2zx + 10xyz - ( 3xy + 5yz - 7zx)`
`= 5xy - 2yz - 2zx + 10xyz - 3xy - 5yz + 7zx`
`text{Rearrange the like terms}`
`= 5xy - 3xy - 2yz - 5yz - 2zx + 7zx + 10xyz`
`= 2xy - 7yz - 5zx + 10xyz`
`text{Answer:}`
`2xy - 7yz - 5zx + 10xyz`.
c) `18 - 3p - 11q + 5pq - 2pq^2 + 5p^2q - ( 4p^2q`` - 3pq + 5pq^2 - 8p + 7q - 10)`
`= 18 - 3p - 11q + 5pq - 2pq^2 + 5p^2q - 4p^2q`` + 3pq - 5pq^2 + 8q - 7q + 10`
`text{Rearrange the like terms}`
`= 18 + 10 - 3p + 8p -11q - 7q + 5pq + 3pq`` - 2pq^2 - 5pq^2 + 5p^2q - 4p^2q`
`= 28 + 5p - 18q + 8pq - 7pq^2 - 4p^2q`` + p^2q`
`= p^2q - 7pq^2 + 8pq -18pq - 18q + 5p + 28`
`text{Answer:}`
`= p^2q - 7pq^2 + 8pq -18pq - 18q + 5p + 28`
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