Exercise 12.1 Page: 234

1. Get the algebraic expressions in the following cases using variables, constants and arithmetic operations.

(i) Subtraction of z from y.

Solution:-

= Y – z

(ii) One-half of the sum of numbers x and y.

Solution:-

= ½ (x + y)

= (x + y)/2

(iii) The number z multiplied by itself.

Solution:-

= z × z

= z²

(iv) One-fourth of the product of numbers p and q.

Solution:-

= ¼ (p × q)

= pq/4

(v) Numbers x and y both squared and added.

Solution:-

= x² + y²

(vi) Number 5 added to three times the product of numbers m and n.

Solution:-

= 3mn + 5

(vii) Product of numbers y and z subtracted from 10.

Solution:-

= 10 – (y × z)

= 10 – yz

(viii) Sum of numbers a and b subtracted from their product.

Solution:-

= (a × b) – (a + b)

= ab – (a + b)

2. (i) Identify the terms and their factors in the following expressions

Show the terms and factors by tree diagrams.

(a) x – 3

Solution:-

Expression: x – 3

Terms: x, -3

Factors: x; -3

b) 1 + x + x²

Solution:-

Expression: 1 + x + x²

Terms: 1, x, x²

Factors: 1; x; x,x

(c) y – y³

Solution:-

Expression: y – y³

Terms: y, -y³

Factors: y; -y, -y, -y

(d) 5xy² + 7x²y

Solution:-

Expression: 5xy² + 7x²y

Terms: 5xy², 7x²y

Factors: 5, x, y, y; 7, x, x, y

(e) – ab + 2b² – 3a²

Solution:-

Expression: -ab + 2b² – 3a²

Terms: -ab, 2b², -3a²

Factors: -a, b; 2, b, b; -3, a, a

(ii) Identify terms and factors in the expressions given below:

(a) – 4x + 5 (b) – 4x + 5y (c) 5y + 3y² (d) xy + 2x²y²

(e) pq + q (f) 1.2 ab – 2.4 b + 3.6 a (g) ¾ x + ¼

(h) 0.1 p² + 0.2 q²

Solution:-

Expressions is defined as, numbers, symbols and operators (such as +. – , × and ÷) grouped together that show the value of something.

In algebra a term is either a single number or variable, or numbers and variables multiplied together. Terms are separated by + or – signs or sometimes by division.

Factors is defined as, numbers we can multiply together to get another number.

3. Identify the numerical coefficients of terms (other than constants) in the following expressions:

(i) 5 – 3t² (ii) 1 + t + t² + t³ (iii) x + 2xy + 3y (iv) 100m + 1000n (v) – p²q² + 7pq (vi) 1.2 a + 0.8 b (vii) 3.14 r² (viii) 2 (l + b)

(ix) 0.1 y + 0.01 y²

Solution:-

Expressions is defined as, numbers, symbols and operators (such as +. – , × and ÷) grouped together that show the value of something.

In algebra a term is either a single number or variable, or numbers and variables multiplied together. Terms are separated by + or – signs or sometimes by division.

A coefficient is a number used to multiply a variable (2x means 2 times x, so 2 is a coefficient) Variables on their own (without a number next to them) actually have a coefficient of 1 (x is really 1x)

4. (a) Identify terms which contain x and give the coefficient of x.

(i) y²x + y (ii) 13y² – 8yx (iii) x + y + 2

(iv) 5 + z + zx (v) 1 + x + xy (vi) 12xy² + 25

(vii) 7x + xy²

Solution:-

(b) Identify terms which contain y² and give the coefficient of y².

(i) 8 – xy² (ii) 5y² + 7x (iii) 2x²y – 15xy² + 7y²

Solution:-

5. Classify into monomials, binomials and trinomials.

(i) 4y – 7z

Solution:-

Binomial.

An expression which contains two unlike terms is called a binomial.

(ii) y²

Solution:-

Monomial.

An expression with only one term is called a monomial.

(iii) x + y – xy

Solution:-

Trinomial.

An expression which contains three terms is called a trinomial.

(iv) 100

Solution:-

Monomial.

An expression with only one term is called a monomial.

(v) ab – a – b

Solution:-

Trinomial.

An expression which contains three terms is called a trinomial.

(vi) 5 – 3t

Solution:-

Binomial.

An expression which contains two unlike terms is called a binomial.

(vii) 4p²q – 4pq²

Solution:-

Binomial.

An expression which contains two unlike terms is called a binomial.

(viii) 7mn

Solution:-

Monomial.

An expression with only one term is called a monomial.

(ix) z² – 3z + 8

Solution:-

Trinomial.

An expression which contains three terms is called a trinomial.

(x) a² + b²

Solution:-

Binomial.

An expression which contains two unlike terms is called a binomial.

(xi) z² + z

Solution:-

Binomial.

An expression which contains two unlike terms is called a binomial.

(xii) 1 + x + x²

Solution:-

Trinomial.

An expression which contains three terms is called a trinomial.

6. State whether a given pair of terms is of like or unlike terms.

(i) 1, 100

Solution:-

Like term.

When term have the same algebraic factors, they are like terms.

(ii) –7x, (5/2)x

Solution:-

Like term.

When term have the same algebraic factors, they are like terms.

(iii) – 29x, – 29y

Solution:-

Unlike terms.

The terms have different algebraic factors, they are unlike terms.

(iv) 14xy, 42yx

Solution:-

Like term.

When term have the same algebraic factors, they are like terms.

(v) 4m²p, 4mp²

Solution:-

Unlike terms.

The terms have different algebraic factors, they are unlike terms.

(vi) 12xz, 12x²z²

Solution:-

Unlike terms.

The terms have different algebraic factors, they are unlike terms.

7. Identify like terms in the following:

(a) – xy², – 4yx², 8x², 2xy², 7y, – 11x², – 100x, – 11yx, 20x²y, – 6x², y, 2xy, 3x

Solution:-

When term have the same algebraic factors, they are like terms.

They are,

– xy², 2xy²

– 4yx², 20x²y

8x², – 11x², – 6x²

7y, y

– 100x, 3x

– 11yx, 2xy

(b) 10pq, 7p, 8q, – p²q², – 7qp, – 100q, – 23, 12q²p², – 5p², 41, 2405p, 78qp,

13p²q, qp², 701p²

Solution:-

When term have the same algebraic factors, they are like terms.

They are,

10pq, – 7qp, 78qp

7p, 2405p

8q, – 100q

– p²q², 12q²p²

– 23, 41

– 5p², 701p²

13p²q, qp²