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## Tamilnadu Samacheer Kalvi 7th Maths Solutions Term 2 Chapter 3 Algebra Ex 3.3

Question 1.

Fill in the blanks.

(i) The degree of the term a^{3}b^{2}c^{4}d^{2} is _______

(ii) Degree of the constant term is _______

(iii) The coefficient of leading term of the expression 3z^{2}y + 2x – 3 is _______

Answers:

(i) 11

(ii) 0

(iii) 3

Identifying the Degree and Leading Coefficient Calculator of Polynomials.

Question 2.

Say True or False.

(i) The degree of m^{2} n and mn^{2} are equal.

(ii) 7a^{2}b and -7ab^{2} are like terms.

(iii) The degree of the expression -4x^{2} yz is -4

(iv) Any integer can be the degree of the expression.

Answers:

(i) True

(ii) False

(iii) False

(iv) True

Question 3.

Find the degree of the following terms.

(i) 5x^{2}

(ii) -7 ab

(iii) 12pq^{2} r^{2}

(iv) -125

(v) 3z

Solution:

(i) 5x^{2}

In 5x^{2}, the exponent is 2. Thus the degree of the expression is 2.

(ii) -7ab

In -7ab, the sum of powers of a and b is 2. (That is 1 + 1 = 2).

Thus the degree of the expression is 2.

(iii) 12pq^{2} r^{2}

In 12pq^{2} r^{2}, the sum of powers of p, q and r is 5. (That is 1 +2 + 2 = 5).

Thus the degree of the expression is 5.

(iv) -125

Here – 125 is the constant term. Degree of constant term is 0.

∴ Degree of -125 is 0.

(v) 3z

The exponent is 3z is 1.

Thus the degree of the expression is 1.

Question 4.

Find the degree of the following expressions.

(i) x^{3} – 1

(ii) 3x^{2} + 2x + 1

(iii) 3t^{4} – 5st^{2} + 7s^{2}t^{2}

(iv) 5 – 9y + 15y2 – 6y3

(v) u^{5} + u^{4}v + u^{3}v^{2} + u_{2}v^{3} + uv^{4}

Solution:

(i) x^{3} – 1

The terms of the given expression are x^{3}, -1

Degree of each of the terms: 3,0

Terms with highest degree: x^{3}.

Therefore, degree of the expression is 3.

(ii) 3x^{2} + 2x + 1

The terms of the given expression are 3x^{2}, 2x, 1

Degree of each of the terms: 2, 1, 0

Terms with highest degree: 3x^{2}

Therefore, degree of the expression is 2.

(iii) 3t^{4} – 5st^{2} + 7s^{2}t^{2}

The terms of the given expression are 3t^{4}, – 5st^{2}, 7s^{3}t^{2}

Degree of each of the terms: 4, 3, 5

Terms with highest degree: 7s^{2}t^{2}

Therefore, degree of the expression is 5.

(iv) 5 – 9y + 15y^{2} – 6y^{3}

The terms of the given expression are 5, – 9y , 15y^{2}, – 6y^{3}

Degree of each of the terms: 0, 1, 2, 3

Terms with highest degree: – 6y^{3}

Therefore, degree of the expression is 3.

(v) u^{5} + u^{4}v + u^{3}v^{2} + u_{2}v^{3} + uv^{4}

The terms of the given expression are u^{5}, u^{4}v , u^{3}v^{2}, u^{2}v^{3}, uv^{4}

Degree of each of the terms: 5, 5, 5, 5, 5

Terms with highest degree: u^{5}, u^{4}v , u^{3}v^{2}, u^{2}v^{3}, uv^{4}

Therefore, degree of the expression is 5.

Question 5.

Identify the like terms : 12x^{3}y^{2}z, – y^{3}x^{2}z, 4z^{3}y^{2}x, 6x^{3}z^{2}y, -5y^{3}x^{2}z

Solution:

-y^{3} x^{2}z and -5y^{3}x^{2}z are like terms.

Question 6.

Add and find the degree of the following expressions.

(i) (9x + 3y) and (10x – 9y)

(ii) (k^{2} – 25k + 46) and (23 – 2k^{2} + 21 k)

(iii) (3m^{2}n + 4pq^{2}) and (5nm^{2} – 2q^{2}p)

Solution:

(i) (9x + 3y) and (10x – 9y)

This can be written as (9x + 3y) + (10x – 9y)

Grouping the like terms, we get

(9x + 10x) + (3y – 9y) = x(9 + 10) + y(3 – 0) = 19x + y(-6) = 19x – 6y

Thus degree of the expression is 1.

(ii) (k^{2} – 25k + 46) and (23 – 2k^{2} + 21k)

This can be written as (k^{2} – 25k + 46) + (23 – 2k^{2} + 21k)

Grouping the like terms, we get

(k^{2} – 2k^{2}) + (-25 k + 21 k) + (46 + 23)

= k^{2} (1 – 2) + k(-25 + 21) + 69 = – 1k^{2} – 4k + 69

Thus degree of the expression is 2.

(iii) (3m^{2}n + 4pq^{2}) and (5nm^{2} – 2q^{2}p)

This can be written as (3m^{2}n + 4pq^{2}) + (5nm^{2} – 2q^{2}p)

Grouping the like terms, we get

(3m^{2}n + 5m^{2}n) + (4pq^{2} – 2pq^{2})

= m^{2}n(3 + 5) + pq^{2}(4 – 2) = 8m^{2}n + 2pq^{2}

Thus degree of the expression is 3.

Question 7.

Simplify and find the degree of the following expressions.

(i) 10x^{2} – 3xy + 9y^{2} – (3x^{2} – 6xy – 3y^{2})

(ii) 9a^{4} – 6a^{3} – 6a^{4} – 3a^{2} + 7a^{3} + 5a^{2}

(iii) 4x^{2} – 3x – [8x – (5x^{2} – 8)]

Solution:

(i) 10x^{2} – 3xy + 9y^{2} – (3x^{2} – 6xy – 3y^{2})

= 10x^{2} – 3xy + 9y^{2} + (-3x^{2} + 6xy + 3y^{2})

= 10x^{2} – 3xy + 9y^{2} – 3x^{2} + 6xy + 3y^{2}

= (10x^{2} – 3x^{2}) + (- 3xy + 6xy) + (9y^{2} + 3y^{2})

= x^{2}(10 – 3) + xy(-3 + 6) + y^{2}(9 + 3)

= x^{2}(7) + xy(3) + y^{2}(12)

Hence, the degree of the expression is 2.

(ii) 9a^{4} – 6a^{3} – 6a^{4} – 3a^{2} + 7a^{3} + 5a^{2}

= (9a^{4} – 6a^{4}) + (- 6a^{3} + 7a^{3}) + (- 3a^{2} + 5a^{2})

= a^{4}(9-6) + a^{3} (- 6 + 7) + a^{2}(-3 + 5)

= 3a^{4} + a^{3} + 2a^{2}

Hence, the degree of the expression is 4.

(iii) 4x^{2} – 3x – [8x – (5x^{2} – 8)]

= 4x^{2} – 3x – [8x + -5x^{2} + 8)]

= 4x^{2} – 3x – [8x – 5x^{2} – 8]

= 4x^{2} – 3x – 8x + 5x^{2} – 8

(4x^{2} + 5x^{2}) + (- 3x – 8x) – 8

= x^{2}(4+ 5) + x(-3-8) – 8

= x^{2}(9) + x(- 11) – 8

= 9x^{2} – 11x – 8

Hence, the degree of the expression is 2.

Objective Type Question

Question 8.

3p^{2} – 5pq + 2q^{2} + 6pq – q^{2} +pq is a

(i) Monomial

(ii) Binomial

(iii) Trinomial

(iv) Quadrinomial

Answer:

(iii) Trinomial

Question 9.

The degree of 6x^{7} – 7x^{3} + 4 is

(i) 7

(ii) 3

(iii) 6

(iv) 4

Answer:

(i) 7

Question 10.

If p(x) and q(x) are two expressions of degree 3, then the degree of p(x) + q(x) is

(i) 6

(ii) 0

(iii) 3

(iv) Undefined

Answer:

(iii) 3