Class 10 Maths Chapter 2 Polynomials – Exercise 2.1 NCERT Solutions

Introduction

Exercise 2.1 introduces polynomials and their identities. You’ll learn how to expand and simplify expressions using standard algebraic identities, and apply them to solve problems efficiently. This exercise builds the foundation for factorization and polynomial equations.

Formula Used

• Standard Identities:

$$(x+y{)}^2=x^2+2xy+y^2$$

$$(x-y{)}^2=x^2-2xy+y^2$$

$$(x+y)(x-y)=x^2-y^2$$

$$(x+a)(x+b)=x^2+(a+b)x+ab$$

NCERT Questions with Solutions (10)

Q1. Expand $(x+4)(x+5)$.

Solution:

$$(x+4)(x+5)=x^2+9x+20$$

Q2. Expand $(x+3)(x+7)$.

Solution:

$$(x+3)(x+7)=x^2+10x+21$$

Q3. Expand $(x+1)(x+2)$.

Solution:

$$(x+1)(x+2)=x^2+3x+2$$

Q4. Expand $(x+6)(x+9)$.

Solution:

$$(x+6)(x+9)=x^2+15x+54$$

Q5. Expand $(x+2)(x+8)$.

Solution:

$$(x+2)(x+8)=x^2+10x+16$$

Q6. Expand $(x-3)(x-5)$.

Solution:

$$(x-3)(x-5)=x^2-8x+15$$

Q7. Expand $(x-7)(x-2)$.

Solution:

$$(x-7)(x-2)=x^2-9x+14$$

Q8. Expand $(x-4)(x+6)$.

Solution:

$$(x-4)(x+6)=x^2+2x-24$$

Q9. Expand $(x+11)(x-11)$.

Solution:

$$(x+11)(x-11)=x^2-121$$

Q10. Expand $(x+12)(x+13)$.

Solution:

$$(x+12)(x+13)=x^2+25x+156$$

FAQs (10 from NCERT)

1. Q: What is a polynomial? A: An algebraic expression consisting of variables and coefficients with non‑negative integer powers.

2. Q: What is a quadratic polynomial? A: A polynomial of degree 2, e.g., $a{x}^2+bx+c$.

3. Q: What is an identity? A: An equation true for all values of variables.

4. Q: What is the difference between identity and equation? A: Identity holds for all values; equation holds for specific values.

5. Q: What is factorization? A: Expressing a polynomial as a product of simpler polynomials.

6. Q: What is the degree of a polynomial? A: The highest power of the variable in the polynomial.

7. Q: What is the zero of a polynomial? A: A value of variable that makes the polynomial equal to zero.

8. Q: Why are identities important? A: They simplify calculations and expansions.

9. Q: What is the identity for $(x+y)(x-y)$? A: $x^2-y^2$.

10. Q: Why is this exercise important? A: It builds the foundation for solving polynomial equations and factorization.

Conclusion

Exercise 2.1 has 10 solved questions and 10 FAQs that strengthen your understanding of polynomial identities and expansions. This builds the foundation for factorization and higher‑order polynomial problems in Class 10 Maths.

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