Algebraic Expressions NCERT 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 xy² and factor 5, term x²y and factor 7.
`– 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:

`– 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 y² and factor 3.
`xy + 2x^2\y^2`

Answer: Term xy and factor 1, term x²y² 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 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:

`5 – 3t^2`

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

Answer: Term t and coefficient 1;, term t² and coefficient 1, term t³ 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 p²q² 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: r² 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 y² and coefficient 0.01.

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

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

Question 7: Classify into monomials, binomials and trinomials.

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

Question 9: Identify like terms in the following:

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

Answer: (– xy², 2xy²), (8x², - 11x²), (- 100x, 3x)
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)