NCERT Solutions for Class 8 Maths Chapter 8 – Algebraic Expressions and Identities Ex 8.1

NCERT Solutions for Class 8 Maths Chapter 8 – Algebraic Expressions and Identities Ex 8.1 are given here in simple, step-by-step form. NCERT stands for National Council of Educational Research and Training, the body that makes your textbook. An algebraic expression is made of terms, and each term is built from variables and numbers. This chapter builds the skills you need to add, subtract and multiply expressions and to use identities. Exercise 8.1 is the first exercise. It covers terms and coefficients, the types of expressions, and adding expressions together.

This exercise has 5 questions. You will pick out the terms and their coefficients, sort expressions into monomials, binomials and trinomials, group like terms, and add algebraic expressions. Every question below is solved in short steps, with the final answer in bold. Students can use this page for homework and revision, parents can use it to check the work at home, and teachers can use it in class. A free printable PDF of these solutions is also available for offline study.

NCERT Solutions for Class 8 Maths Chapter 8 – Algebraic Expressions and Identities Ex 8.1

Algebraic Expressions and Identities
Medium
Q.
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
Algebraic Expressions and Identities
Easy
Q.
(a) Add:p(p−q),q(q−r) and r(r−p)(b) Add:2x(z−x−y) and 2y(z−y−x)(c) Subtract : 3l(l−4m+5n) from 4l(10n−3m+2l)(d) Subtract : 3a(a+b+c)−2b(a−b+c)from 4c(−a+b+c)
Algebraic Expressions and Identities
Easy
Q.
Identify the terms, their coefficients for each of the following expressions.
(i) 5xyz2 – 3zy
(ii) 1 + x + x2
(iii) 4x2y2 – 4x2y2z2 + z2
(iv) 3 – pq + qr – rp
(v)x2+y2-xy
(vi) 0.3a – 0.6ab + 0.5b
Algebraic Expressions and Identities
Easy
Q.
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 + 3xy,4z – 15z2,  ab + bc + cd + da, pqr, p2q + pq2, 2p + 2q

NCERT Solutions for Class 8 Maths Chapter 8 – Algebraic Expressions and Identities Ex 8.1

Words You Need to Know

  • A term is a part of an expression separated by a plus or minus sign.
  • The coefficient is the number part of a term. In 5xy, the coefficient is 5.
  • Like terms have the same variable part, such as 7x and −3x. Only like terms can be added or subtracted.
  • A monomial has one term, a binomial has two terms, and a trinomial has three terms. An expression with one or more terms is called a polynomial.
  • To add expressions, write them one below the other with like terms in the same column, then add each column.

Exercise 8.1 – Questions and Answers

Q1. 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

Answer:

(i) Writing the expressions one below the other and adding the like terms column by column:

    ab − bc
         bc − ca
  − ab      + ca
  ─────────────────
         0

The sum is 0.

(ii)

   a − b      + ab
       b − c      + bc
  − a     + c          + ac
  ────────────────────────────
                ab + bc + ac

The sum is ab + bc + ac.

(iii)

   2p²q² − 3pq + 4
  −3p²q² + 7pq + 5
  ──────────────────
   − p²q² + 4pq + 9

The sum is −p²q² + 4pq + 9.

(iv)

   l² + m²
        m² + n²
   l²      + n²
              2lm + 2mn + 2nl
  ──────────────────────────────────
   2l² + 2m² + 2n² + 2lm + 2mn + 2nl

The sum is 2l² + 2m² + 2n² + 2lm + 2mn + 2nl.

Q2. (a) Subtract 4a − 7ab + 3b + 12 from 12a − 9ab + 5b − 3
(b) Subtract 3xy + 5yz − 7zx from 5xy − 2yz − 2zx + 10xyz
(c) Subtract 4p²q − 3pq + 5pq² − 8p + 7q − 10 from 18 − 3p − 11q + 5pq − 2pq² + 5p²q

Answer:
To subtract, write the second expression below the first, change the sign of every term being subtracted, and then add.

(a)

    12a − 9ab + 5b − 3
     4a − 7ab + 3b + 12
    (−)  (+)   (−)  (−)
  ────────────────────────
     8a − 2ab + 2b − 15

The answer is 8a − 2ab + 2b − 15.

(b)

   5xy − 2yz − 2zx + 10xyz
   3xy + 5yz − 7zx
   (−)   (−)   (+)
  ──────────────────────────
   2xy − 7yz + 5zx + 10xyz

The answer is 2xy − 7yz + 5zx + 10xyz.

(c)

   18 − 3p − 11q + 5pq − 2pq² + 5p²q
  −10 − 8p +  7q − 3pq + 5pq² + 4p²q
   (+)  (+)  (−)   (+)   (−)    (−)
  ─────────────────────────────────────
   28 + 5p − 18q + 8pq − 7pq² +  p²q

The answer is 28 + 5p − 18q + 8pq − 7pq² + p²q.

Q3. Identify the terms, their coefficients for each of the following expressions.
(i) 5xyz² − 3zy
(ii) 1 + x + x²
(iii) 4x²y² − 4x²y²z² + z²
(iv) 3 − pq + qr − rp
(v) x/2 + y/2 − xy
(vi) 0.3a − 0.6ab + 0.5b

Answer:

S. no. Terms Coefficients
(i) 5xyz² − 3zy 5xyz² and −3zy 5 and −3
(ii) 1 + x + x² 1, x and x² 1, 1 and 1
(iii) 4x²y² − 4x²y²z² + z² 4x²y², −4x²y²z² and z² 4, −4 and 1
(iv) 3 − pq + qr − rp 3, −pq, qr and −rp 3, −1, 1 and −1
(v) x/2 + y/2 − xy x/2, y/2 and −xy 1/2, 1/2 and −1
(vi) 0.3a − 0.6ab + 0.5b 0.3a, −0.6ab and 0.5b 0.3, −0.6 and 0.5

Q4. 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 + 3xy, 4z − 15z², ab + bc + cd + da, pqr, p²q + pq², 2p + 2q

Answer:
An expression that contains only one term is called a monomial.
An expression that contains two terms is called a binomial.
An expression containing three terms is a trinomial.

Monomials Binomials Trinomials
1000, pqr x + y, 2y − 3y², 4z − 15z², p²q + pq², 2p + 2q 7 + y + 5x, 2y − 3y² + 4y³, 5x − 4y + 3xy

The polynomials x + x² + x³ + x⁴ and ab + bc + cd + da do not fit in any of these three categories, because each of them has four terms.

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