Question

expand by using identities ( 1/4k + 1/2) (1/4k - 1/2)​

Answer 1

1. Which of the following expressions are polynomials in one variable and which are not? State reasons for your answer.

Ans. (i) 4x2 – 3x + 7

⇒ 4x2 – 3x + 7x°

∵ All the exponents of x are whole numbers.

∴ 4x2 – 3x + 7 is a polynomial in one variable.

(ii)

∵ All the exponents of y are whole numbers.

∴ is a polynomial in one variable.

(v) x10 + y3 + t50

∵; Exponent of every variable is a whole number,

∴ x10 + y3 + t50 is a polynomial in x, y and t, i.e. in three variables.

2. Write the co-efficients of x2 in each of the following:

(i) 2 + x2 + x

(ii) 2 – x2 + x3

(iii)

(v)

Ans. (i) 2 + x2 + x

The co-efficient of x2 is 1.

(ii) 2 – x2 + x3

The co-efficient of x2 is (–1).

(iii)

The co-efficient of x2 is

(iv)

∴ The co-efficient of x2 is 0

3. Give one example each of a binomial of degree 35, and of a monomial of degree 100.

Ans. (i) A binomial of degree 35 can be: 3x35 – 4

(ii) A monomial of degree 100 can be:

4. Write the degree of each of the following polynomials:

(i) 5x3 + 4x2 + 7x (ii) 4 - y2 (iii) (iv) 3

Ans. (i) 5x3 + 4x2 + 7x

∵ The highest exponent of x is 3.

∴ The degree of the polynomial is 3.

(ii) 4 – y2

∵ The highest exponent of y is 2.

∴ The degree of the polynomial is 2.

(iii)

∵ The highest exponent of t is 1.

∴ The degree of the polynomial is 1.

(iv) 3

since, 3 = 3x°

∴ The degree of the polynomial 3 is 0.

5. Classify the following as linear, quadratic and cubic polynomials:

(i) x2 + x

(ii) x – x3

(iii) y + y2 + 4

(iv) 1 + x

(v) 3t

(vi) r2

(vii) 7x3

Ans. (i) x2 +x

∵ The degree of x2 + x is 2.

∴ It is a quadratic polynomial.

(ii) x – x3

∵ The degree of x – x3 is 3.

∴ It is a cubic polynomial.

(iii) y + y2 + 4

∵ The degree of y + y2 + 4 is 2.

∴ It is a quadratic polynomial.

(iv) 1 + x

∵ The degree of 1 + x is 1.

∴ It is a linear polynomial.

(v) 3t

∵ The degree of 3t is 1.

∴ It is a linear polynomial.

(vi) r2

∵ The degree of r2 is 2.

∴ It is a quadratic polynomial.

(vii) 7x3

∵ The degree of 7x3 is 3.

∴ It is a cubic polynomial.

Answer 2

Answer:

$(\frac{1}{4k} + \frac{1}{2} )( \frac{1}{4k} - \frac{1}{2} )$

By using identity

(a+b)(a-b)=a^2-b^2

$( { \frac{1}{4k} })^{2} - ( { \frac{1}{2}) }^{2}$

$\frac{1}{ {4k}^{2} } - \frac{1}{4}$

Hope it helps