Algebraic Expressions

Exercise 12.1

Question 1: Get the algebraic expression in the following cases using variables, constants and arithmetic operations.

  1. Subtraction of z from y.

    Answer: `y – z`
  2. One half of the sum of numbers x and y.

    Answer: `(x + y) ÷ 2`
  3. The number z multiplied by itself.

    Answer: `z^2`
  4. One fourth of the product of numbers p and q.

    Answer: `(p × q) ÷ 4`
  5. Numbers x and y both squared and added.

    Answer: `x^2 + y^2`
  6. Number 5 added to three times the product of numbers m and n.

    Answer: `3mn + 5`
  7. Product of numbers y and z subtracted from 10.

    Answer: `10 – yz`
  8. Sum of numbers a and b subtracted from their product.

    Answer: `ab – (a + b)`

Question 2: Identify the terms and their factors in the following expressions. Show the terms and factors by tree diagrams.

  1. `x – 3`

    Answer: term = x and factor = 1
  2. `1 + x + x^2`

    Answer: Term x and factor 1; term x^2 and factor 1
  3. `y – y^3`

    Answer: Term y and factor 1; term y^3 and factor – 1
  4. `5xy^2 + 7x^2\y`

    Answer: Term xy2 and factor 5; term x2y and factor 7.
  5. `– ab + 2b^2 – 3a^2`

    Answer: Term ab and factor – 1; term b2 and factor 2; term a2 and factor – 3

Question 3: Identify terms and factors in the expression given below:

  1. `– 4x + 5`

    Answer: Term x and factor – 4
  2. `– 4x + 5y`

    Answer: Term x and factor – 4; term y and factor 5.
  3. `6y + 3y^2`

    Answer: Term y and factor 6; term y2 and factor 3.
  4. `xy + 2x^2\y^2`

    Answer: Term xy and factor 1; term x2y2 and factor 2.
  5. `pq + q`

    Answer: Term pq and factor 1; term q and factor 1.
  6. `1.2 ab – 2.4 b + 3.6 a`

    Answer: Term ab and factor 1.2; term b and factor 2.4; term a and factor 3.6.
  7. `3/4x + 1/4`

    Answer: Term x and factor ¾ .
  8. `0.1p^2 + 0.2q^2`

    Answer: Term p2 and factor 0.1; term q2 and factor 0.2

Question 4: Identify the numerical coefficients of terms (other than constants) in the following expressions:

  1. `5 – 3t^2`

    Answer: Term t2 and coefficient – 3.
  2. `1 + t + t^2 + t^3`

    Answer: Term t and coefficient 1; term t2 and coefficient 1; term t3 and coefficient 1.
  3. `x + 2xy + 3y`

    Answer: term x and coefficient 1, term xy and coefficient 2; term y and coefficient 3.
  4. `100 m + 1000n`

    Answer: term m and coefficient 100; term n and coefficient 1000.
  5. `– p^2\q^2 + 7pq`

    Answer: term p2q2 and coefficient – 1; term pq and coefficient 7.
  6. `1.2 a + 0.8b`

    Answer: Term a and coefficient 1.2; term b and coefficient 0.8.
  7. `3.14r^2`

    Answer: r2 and coefficient 3.14.
  8. `2(l+b)`

    Answer: Term l and coefficient 2; term b and coefficient 2.
  9. `0.1y + 0.01y^2`

    Answer: Term y and coefficient 0.1; term y2 and coefficient 0.01.

Question 5: Identify terms which contain x and give the coefficient of x.

  1. `y^2 + y`

    Answer: None
  2. `13y^2 – 8yx`

    Answer: -8y
  3. `x + y + 2`

    Answer: 1
  4. `5 + z + zx`

    Answer: z
  5. `1 + x + xy`

    Answer: 1 and y
  6. `12xy^2 + 25`

    Answer: 12y2
  7. `7x + xy^2`

    Answer: 7 and y2

Question 6: Identify the terms which contain y2 and give the coefficient of y2.

  1. `8 – xy^2`

    Answer: x
  2. `5y^2 + 7x`

    Answer: 5
  3. `2x^2\y – 15xy^2 + 7y^2`

    Answer: 7 and 15x

Question 7: Classify into monomials, binomials and trinomials.

  1. `4y – 7z`

    Answer: Binomial
  2. `y^2`

    Answer: monomial
  3. `x + y – xy`

    Answer: Trinomial
  4. `100`

    Answer: Monomial
  5. `ab – a – b`

    Answer: Trinomial
  6. `5 – 3t`

    Answer: Binomial
  7. `4p^2\q – 4pq^2`

    Answer: Binomial
  8. `7mn`

    Answer: Monomial
  9. `z^2 - 3z + 8`

    Answer: Trinomial
  10. `a^2 + b^2`

    Answer: Binomial
  11. `z^2 + z`

    Answer: Binomial
  12. `1 + x + x^2`

    Answer: Trinomial

Question 8: State whether a given pair of terms is of like or unlike terms.

  1. `1,  100`

    Answer: Like terms
  2. `– 7x,  (5/2)x`

    Answer: Like terms
  3. `– 29x,  - 29y`

    Answer: Unlike terms
  4. `14xy,  42yx`

    Answer: Like terms
  5. `4m^2p,  4mp^2`

    Answer: Unlike terms
  6. `12xz,  12x^2\z^2`

    Answer: Unlike terms

Question 9: Identify like terms in the following:

  1. – xy2, - 4yx2, 8x2, 2xy2, 7y, - 11x2, - 100x, - 11yx, 20x2y, - 6x2m y, 2xy, 3x

    Answer: (– xy2, 2xy2), (8x2, - 11x2), (- 100x, 3x)
  2. 10pq, 7p, 8q, - p2q2, - 7qp, - 100q, - 23, 12q2p2, - 5p2, 41, 2405p, 78qp, 13p2q, qp2, 701p2

    Answer: (10pq- 7qp, 78qp), (7p, 2405p), (- p2q2, 12q2p2), (- 23, 41)


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