Class 8 - Mathematics
Algebraic Expressions and Identities - Exercise 9.1
Top Block 1
Question :1. Identify the terms, their coefficients for each of the following expressions:
(i) 5xyz² – 3zy
(ii) 1 + 𝓍 + 𝓍 ²
(iii) 4𝓍²y² – 4𝓍²y²z² + z²
(iv) 3 – pq + qr – rp
(v) x⁄2 + y⁄2 – 𝓍y
(vi) 0.3a – 0.6ab + 0.5b
(i) 5xyz² – 3zy
(ii) 1 + 𝓍 + 𝓍 ²
(iii) 4𝓍²y² – 4𝓍²y²z² + z²
(iv) 3 – pq + qr – rp
(v) x⁄2 + y⁄2 – 𝓍y
(vi) 0.3a – 0.6ab + 0.5b
Answer :
(i) Terms: 5xyz² and – 3zy
Coefficient in :5xyz² is 5 and in – 3zy is – 3z
(ii) Terms: 1, 𝓍 and 𝓍²
Coefficient of 𝓍 and𝓍²coefficient of is 1.
(iii) Terms: 4𝓍²y², -4𝓍²y²z² and z²
Coefficient in : 4𝓍²y² is 4, coefficient of -4𝓍²y²z² is -4 and coefficient of is 1. And coefficient of z².
(iv) Terms: 3 – pq+qr and -rp
Coefficient of is , coefficient of is 1 and coefficient of is
(v) Terms: and )x⁄2, y⁄2and -𝓍y
Coefficient of is 1 coefficient ofy⁄2 is 1 and coefficient of -𝓍y is -1.
(vi) Terms: 0.3a, – 0.6ab and 0.5b
Coefficient of 0.3a is 0.3, coefficient of – 0.6ab is and coefficient of 5bis 0.5.
(i) Terms: 5xyz² and – 3zy
Coefficient in :5xyz² is 5 and in – 3zy is – 3z
(ii) Terms: 1, 𝓍 and 𝓍²
Coefficient of 𝓍 and𝓍²coefficient of is 1.
(iii) Terms: 4𝓍²y², -4𝓍²y²z² and z²
Coefficient in : 4𝓍²y² is 4, coefficient of -4𝓍²y²z² is -4 and coefficient of is 1. And coefficient of z².
(iv) Terms: 3 – pq+qr and -rp
Coefficient of is , coefficient of is 1 and coefficient of is
(v) Terms: and )x⁄2, y⁄2and -𝓍y
Coefficient of is 1 coefficient ofy⁄2 is 1 and coefficient of -𝓍y is -1.
(vi) Terms: 0.3a, – 0.6ab and 0.5b
Coefficient of 0.3a is 0.3, coefficient of – 0.6ab is and coefficient of 5bis 0.5.
Question :2. Classify the following polynomials as monomials, binomials, trinomials. Which polynomials do not fit in any of these three categories: x + y ,
1000, x + x²+x³+ x4, 7 + y + 5x, 2y -3y², 2y – 3y²+ 4y³, 5x-4y+3sy, 4z-15z², ab+bc+cd+da, pqr, p²q + pq², 2p + 2q
1000, x + x²+x³+ x4, 7 + y + 5x, 2y -3y², 2y – 3y²+ 4y³, 5x-4y+3sy, 4z-15z², ab+bc+cd+da, pqr, p²q + pq², 2p + 2q
Answer :
(i) Since x + y contains two terms. Therefore it is binomial.
(ii) Since 1000 contains one terms. Therefore it is monomial.
(iii) Since x + x²+x³+ x4 contains four terms. Therefore it is a polynomial and it does not fit in above three categories.
(iv) Since7 + y + 5xcontains three terms. Therefore it is trinomial.
(v) Since 2y -3y²contains two terms. Therefore it is binomial.
(vi) Since2y – 3y²+ 4y³contains three terms. Therefore it is trinomial.
(vii) Since5x – 4y + 3sy contains three terms. Therefore it is trinomial.
(viii) Since4z-15z² contains two terms. Therefore it is binomial.
(ix) Sinceab+bc+cd+da contains four terms. Therefore it is a polynomial and it does not fit in above three categories.
(x) Since pqr contains one terms. Therefore it is monomial.
(xi) Since p²q + pq² contains two terms. Therefore it is binomial.
(xii) Since 2p + 2q contains two terms. Therefore it is binomial..
(i) Since x + y contains two terms. Therefore it is binomial.
(ii) Since 1000 contains one terms. Therefore it is monomial.
(iii) Since x + x²+x³+ x4 contains four terms. Therefore it is a polynomial and it does not fit in above three categories.
(iv) Since7 + y + 5xcontains three terms. Therefore it is trinomial.
(v) Since 2y -3y²contains two terms. Therefore it is binomial.
(vi) Since2y – 3y²+ 4y³contains three terms. Therefore it is trinomial.
(vii) Since5x – 4y + 3sy contains three terms. Therefore it is trinomial.
(viii) Since4z-15z² contains two terms. Therefore it is binomial.
(ix) Sinceab+bc+cd+da contains four terms. Therefore it is a polynomial and it does not fit in above three categories.
(x) Since pqr contains one terms. Therefore it is monomial.
(xi) Since p²q + pq² contains two terms. Therefore it is binomial.
(xii) Since 2p + 2q contains two terms. Therefore it is binomial..
Question: 3. Add the following:
(i) ab-bc, bc-ca, ca-ab
(ii) a – b + ab, b – c + bc, c – a + ac
(iii) 2p²q² – 3pq + 4, 5 + 7pq – 3p²q²
(iv) l²+m², m² + n², n²+l² + 2lm + 2mn + 2nl
(i) ab-bc, bc-ca, ca-ab
(ii) a – b + ab, b – c + bc, c – a + ac
(iii) 2p²q² – 3pq + 4, 5 + 7pq – 3p²q²
(iv) l²+m², m² + n², n²+l² + 2lm + 2mn + 2nl
Answer :
(i) ab-bc, bc-ca, ca-ab
(i) ab-bc, bc-ca, ca-ab
(ii) a – b + ab, b – c + bc, c – a + ac
Mddle block 1
(iii) 2p²q² – 3pq + 4, 5 + 7pq – 3p²q²
(iv) l²+m², m² + n², n² + l² + 2lm + 2mn + 2nl
Question: 4. (a) Subtract 4a – 7ab + 3b + 12 from 12 – 9ab – 5b + 1
(b) Subtract 3xy + 5yz – 7zx from 5xy – 2yz – 2zx + 10syz
(c) Subtract 4p²q 3pa + 5pq² – 8p + 7q – 10 from 18 – 3p – 11q + 5pq – 2pq² + 5p²q
(b) Subtract 3xy + 5yz – 7zx from 5xy – 2yz – 2zx + 10syz
(c) Subtract 4p²q 3pa + 5pq² – 8p + 7q – 10 from 18 – 3p – 11q + 5pq – 2pq² + 5p²q
Answer :
(a) Subtract 4a – 7ab + 3b + 12 from12 – 9ab – 5b + 1
(a) Subtract 4a – 7ab + 3b + 12 from12 – 9ab – 5b + 1
(b) Subtract 3xy + 5yz – 7zx from 5xy – 2yz – 2zx + 10syz
(c) Subtract 4p²q 3pa + 5pq² – 8p + 7q – 10 from 18 – 3p – 11q + 5pq – 2pq² + 5p²q
