# Algebraic Expressions

## Exercise 12.1

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

- Subtraction of z from y.
**Answer:**`y – z` - One half of the sum of numbers x and y.
**Answer:**`(x + y) ÷ 2` - The number z multiplied by itself.
**Answer:**`z^2` - One fourth of the product of numbers p and q.
**Answer:**`(p × q) ÷ 4` - Numbers x and y both squared and added.
**Answer:**`x^2 + y^2` - Number 5 added to three times the product of numbers m and n.
**Answer:**`3mn + 5` - Product of numbers y and z subtracted from 10.
**Answer:**`10 – yz` - 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.

- `x – 3`
**Answer:**term = x and factor = 1 - `1 + x + x^2`
**Answer:**Term x and factor 1, term `x^2` and factor 1 - `y – y^3`
**Answer:**Term y and factor 1, term `y^3` and factor – 1 - `5xy^2 + 7x^2\y`
**Answer:**Term xy^{2}and factor 5, term x^{2}y and factor 7. - `– ab + 2b^2 – 3a^2`
**Answer:**Term ab and factor – 1, term b^{2}and factor 2, term a^{2}and factor – 3

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

- `– 4x + 5`
**Answer:**Term x and factor – 4 - `– 4x + 5y`
**Answer:**Term x and factor – 4, term y and factor 5. - `6y + 3y^2`
**Answer:**Term y and factor 6, term y^{2}and factor 3. - `xy + 2x^2\y^2`
**Answer:**Term xy and factor 1, term x^{2}y^{2}and factor 2. - `pq + q`
**Answer:**Term pq and factor 1, term q and factor 1. - `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. - `3/4x + 1/4`
**Answer:**Term x and factor ¾ . - `0.1p^2 + 0.2q^2`
**Answer:**Term p^{2}and factor 0.1, term q^{2}and factor 0.2

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

- `5 – 3t^2`
**Answer:**Term t^{2}and coefficient – 3. - `1 + t + t^2 + t^3`
**Answer:**Term t and coefficient 1;, term t^{2}and coefficient 1, term t^{3}and coefficient 1. - `x + 2xy + 3y`
**Answer:**term x and coefficient 1, term xy and coefficient 2, term y and coefficient 3. - `100 m + 1000n`
**Answer:**term m and coefficient 100, term n and coefficient 1000. - `– p^2\q^2 + 7pq`
**Answer:**term p^{2}q^{2}and coefficient – 1, term pq and coefficient 7. - `1.2 a + 0.8b`
**Answer:**Term a and coefficient 1.2, term b and coefficient 0.8. - `3.14r^2`
**Answer:**r^{2}and coefficient 3.14. - `2(l+b)`
**Answer:**Term l and coefficient 2, term b and coefficient 2. - `0.1y + 0.01y^2`
**Answer:**Term y and coefficient 0.1, term y^{2}and coefficient 0.01.

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

- `y^2 + y`
**Answer:**None - `13y^2 – 8yx`
**Answer:**-8y - `x + y + 2`
**Answer:**1 - `5 + z + zx`
**Answer:**z - `1 + x + xy`
**Answer:**1 and y - `12xy^2 + 25`
**Answer:**12y^{2} - `7x + xy^2`
**Answer:**7 and y^{2}

**Question 6:** Identify the terms which contain y^{2} and give the coefficient of y^{2}.

- `8 – xy^2`
**Answer:**x - `5y^2 + 7x`
**Answer:**5 - `2x^2\y – 15xy^2 + 7y^2`
**Answer:**7 and 15x

**Question 7:** Classify into monomials, binomials and trinomials.

- `4y – 7z`
**Answer:**Binomial - `y^2`
**Answer:**monomial - `x + y – xy`
**Answer:**Trinomial - `100`
**Answer:**Monomial - `ab – a – b`
**Answer:**Trinomial - `5 – 3t`
**Answer:**Binomial - `4p^2\q – 4pq^2`
**Answer:**Binomial - `7mn`
**Answer:**Monomial - `z^2 - 3z + 8`
**Answer:**Trinomial - `a^2 + b^2`
**Answer:**Binomial - `z^2 + z`
**Answer:**Binomial - `1 + x + x^2`
**Answer:**Trinomial

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

- `1, 100`
**Answer:**Like terms - `– 7x, (5/2)x`
**Answer:**Like terms - `– 29x, - 29y`
**Answer:**Unlike terms - `14xy, 42yx`
**Answer:**Like terms - `4m^2p, 4mp^2`
**Answer:**Unlike terms - `12xz, 12x^2\z^2`
**Answer:**Unlike terms

**Question 9:** Identify like terms in the following:

- – xy
^{2}, - 4yx^{2}, 8x^{2}, 2xy^{2}, 7y, - 11x^{2}, - 100x, - 11yx, 20x^{2}y, - 6x^{2}m y, 2xy, 3x**Answer:**(– xy^{2}, 2xy^{2}), (8x^{2}, - 11x^{2}), (- 100x, 3x) - 10pq, 7p, 8q, - p
^{2}q^{2}, - 7qp, - 100q, - 23, 12q^{2}p^{2}, - 5p^{2}, 41, 2405p, 78qp, 13p^{2}q, qp^{2}, 701p^{2}**Answer:**(10pq- 7qp, 78qp), (7p, 2405p), (- p^{2}q^{2}, 12q^{2}p^{2}), (- 23, 41)