Algebraic expressions and identities class 8 exercise 9.1 solution Answer of all Question 2023

Algebraic expressions and identities class 8 exercise 9.1 solution Answer of all Question 

1. Algebraic Expression:

   - An algebraic expression is a mathematical phrase that can contain numbers, variables, and operations (such as addition, subtraction, multiplication, and division).

   - For example, (3x + 5) and (2y - 7) are algebraic expressions. Here, (x) and (y) are variables, and the numbers 3, 5, 2, and 7 are constants.

2. Identities:

   - An identity is a mathematical statement that is true for all values of the variables involved.

   - In algebra, you often encounter algebraic identities, which are equations that hold true for any values of the variables. They are like mathematical truths.

   - For example, the distributive property is an identity: (a(b + c) = ab + ac). This is true for any values of (a), (b), and (c).

In Class 8, students start working with simple algebraic expressions and learn to manipulate them using various algebraic identities. Understanding these concepts is crucial as they form the foundation for more advanced algebraic topics in higher classes. Students also learn how to simplify expressions, solve equations, and apply these concepts to solve real-world problems.

Class 8 Maths Chapter 9 exercise 9.1 Question 1 - Algebraic Expressions and Identities

Ex 9.1 Class 8 Maths Question 1

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

Ex 9.1 Class 8 Maths Question 1 Solution Answer

To identify the terms and their coefficients in each expression, let's break down each expression:

(i) $5��{�}^2-3��$

• Terms:

  • $5��{�}^2$ (1st term)
  • $-3��$ (2nd term)

• Coefficients:

  • For the 1st term, the coefficient is $5$.
  • For the 2nd term, the coefficient is $-3$.

(ii) $1+�+{�}^2$

• Terms:

  • $1$ (1st term)
  • $�$ (2nd term)
  • ${�}^2$ (3rd term)

• Coefficients:

  • For the 1st term, the coefficient is $1$.
  • For the 2nd term, the coefficient is $1$ (implicitly, as $�$ without a coefficient is the same as $1�$).
  • For the 3rd term, the coefficient is $1$ (implicitly, as ${�}^2$ is the same as $1{�}^2$).

(iii) $4{�}^2{�}^2-4{�}^2{�}^2{�}^2+{�}^2$

• Terms:

  • $4{�}^2{�}^2$ (1st term)
  • $-4{�}^2{�}^2{�}^2$ (2nd term)
  • ${�}^2$ (3rd term)

• Coefficients:

  • For the 1st term, the coefficient is $4$.
  • For the 2nd term, the coefficient is $-4$.
  • For the 3rd term, the coefficient is $1$ (implicitly, as ${�}^2$ is the same as $1{�}^2$).

(iv) $3-��+��-��$

• Terms:

  • $3$ (1st term)
  • $-��$ (2nd term)
  • $��$ (3rd term)
  • $-��$ (4th term)

• Coefficients:

  • For the 1st term, the coefficient is $3$.
  • For the 2nd term, the coefficient is $-1$ (implicitly, as $-��$ is the same as $-1��$).
  • For the 3rd term, the coefficient is $1$ (implicitly, as $��$ is the same as $1��$).
  • For the 4th term, the coefficient is $-1$ (implicitly, as $-��$ is the same as $-1��$).

(v) ${�}^2+{�}^2-��$

• Terms:

  • ${�}^2$ (1st term)
  • ${�}^2$ (2nd term)
  • $-��$ (3rd term)

• Coefficients:

  • For the 1st term, the coefficient is $1$ (implicitly, as ${�}^2$ is the same as $1{�}^2$).
  • For the 2nd term, the coefficient is $1$ (implicitly, as ${�}^2$ is the same as $1{�}^2$).
  • For the 3rd term, the coefficient is $-1$ (implicitly, as $-��$ is the same as $-1��$).

(vi) $0.3�-0.6��+0.5�$

• Terms:

  • $0.3�$ (1st term)
  • $-0.6��$ (2nd term)
  • $0.5�$ (3rd term)

• Coefficients:

• For the 1st term, the coefficient is $0.3$.
• For the 2nd term, the coefficient is $-0.6$.
• For the 3rd term, the coefficient is $0.5$.
• 
  

Ex 9.1 Class 8 Maths Question 2.

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

Ex 9.1 Class 8 Maths Question 2 solution Answer

Let's classify each given polynomial:

1. $�+�$

   • Classification: Binomial

2. $1000$

   • Classification: Monomial

3. $�+{�}^2+{�}^3+{�}^4$

   • Classification: Polynomial (but not a monomial, binomial, or trinomial)

4. $7+�+5�$

   • Classification: Trinomial

5. $2�-3{�}^2$

   • Classification: Binomial

6. $2�-3{�}^2+4{�}^3$

   • Classification: Polynomial (but not a monomial, binomial, or trinomial)

7. $5�-4�+3��$

   • Classification: Trinomial

8. $4�-15{�}^2$

   • Classification: Binomial

9. $��+��+��+��$

   • Classification: Polynomial (but not a monomial, binomial, or trinomial)

10. $���$

    • Classification: Monomial

11. ${�}^2�+�{�}^2$

    • Classification: Binomial

12. $2�+2�$

    • Classification: Binomial

To summarize:

• Monomials have one term.
• Binomials have two terms.
• Trinomials have three terms.
• Any polynomial with more than three terms is simply called a polynomial but does not fall into the specific categories of monomial, binomial, or trinomial.

Ex 9.1 Class 8 Maths Question 3.

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

Ex 9.1 Class 8 Maths Question 3. Solution Answer

(i) $��-��+��-��+��-��$

Combine like terms:

$��$ and $-��$ cancel each other out. Similarly, $��$ and $-��$ as well as $��$ and $-��$ cancel each other out.

The sum is $0$.

(ii) $�-�+��+�-�+��+�-�+��$

Combine like terms:

Group the terms with common variables:

$�-�+�-�+�-�+��+��+��$

Combine the like terms: $�-�$, $�-�$, and $�-�$ all equal $0$. We are left with $��+��+��$.

So, the sum is $��+��+��$.

(iii) $2{�}^2{�}^2-3��+4+5+7��-3{�}^2{�}^2$

Combine like terms:

$2{�}^2{�}^2-3{�}^2{�}^2+7��-3��+4+5$

Combine the like terms: $-3{�}^2{�}^2+4��+9$.

So, the sum is $-{�}^2{�}^2+4��+9$.

(iv) ${�}^2+{�}^2+{�}^2+{�}^2+{�}^2+{�}^2+2��+2��+2��$

Combine like terms:

$2{�}^2+2{�}^2+2{�}^2+2��+2��+2��$

This is the simplified form of the given expression, where like terms are combined.

So, the sum is $2{�}^2+2{�}^2+2{�}^2+2��+2��+2��$.

Ex 9.1 Class 8 Maths Question 4.

(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

Ex 9.1 Class 8 Maths Question 4.Solution / Answer:

(a) Subtract $4�-7��+3�+12$ from $12�-9��+5�-3$:

$(12�-9��+5�-3)-(4�-7��+3�+12)$

Combine like terms:

$12�-9��+5�-3-4�+7��-3�-12$

Group the like terms:

$(12�-4�)+(-9��+7��)+(5�-3�)+(-3-12)$

Combine further:

$8�-2��+2�-15$

So, the result is $8�-2��+2�-15$.

(b) Subtract $3��+5��-7��$ from $5��-2��-2��+10���$:

$(5��-2��-2��+10���)-(3��+5��-7��)$

Combine like terms:

$5��-2��-2��+10���-3��-5��+7��$

Group the like terms:

$(5��-3��)+(-2��-5��)+(-2��+7��)+10���$

Combine further:

$2��-7��+5��+10���$

So, the result is $2��-7��+5��+10���$.

(c) Subtract $4{�}^2�-3��+5�{�}^2-8�+7�-10$ from $18-3�-11�+5��-2�{�}^2+5{�}^2�$:

$(18-3�-11�+5��-2�{�}^2+5{�}^2�)-(4{�}^2�-3��+5�{�}^2-8�+7�-10)$

Combine like terms:

$18-3�-11�+5��-2�{�}^2+5{�}^2�-4{�}^2�+3��-5�{�}^2+8�-7�+10$

Group the like terms:

$(18)+(-3�+8�)+(-11�-7�)+(5��+3��-4{�}^2�)+(-2�{�}^2-5�{�}^2)+5{�}^2�+10$

Combine further:

$18+5�-18�-{�}^2�-7�{�}^2+5{�}^2�+10$

So, the result is $-{�}^2�-2�{�}^2+5{�}^2�+5�-8�+28$.

Class 8Maths Exercise 9.2 Solutions

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