**GSEB Solutions for Class 6 Mathematics – Polynomial**

GSEB SolutionsMathsScience

**Activity**

**Solution 1:**

- 4x
^{2}, 7x^{2}and 2x^{2} - -y
^{3}, -y^{3}and 3y^{3} - 2xy
^{2}and 3xy^{2} - 6x
^{7}and x^{7}

**Solution 2:**

- 5x, 2x
^{2} - -3x, 7x
^{2} - 8xy
^{3}, 8yx^{3} - a
^{2}b^{2}, 7ab - -x, 5x

**Solution 3:**

4x^{2}, -y^{2}

4b^{2}, p^{2}

4x^{2}, p^{2}

(Note: Many more answers are possible.)

**Exercise **

**Solution 1:**

**Solution 2:**

The polynomials having constant terms are given below.

4x^{2} + 2x – 3, x + 4, 6a^{2} + 5ab + 7, 16, 6x^{2} – 6x + 5

**Solution 3:**

(1) The pairs of like terms are: __4x ^{2}__and

__3x__;

^{2}__– x__and

__– 2x.__

(2) The pairs of like terms are:

__– 8x__and

^{2}__7x__;

^{2}__7x__and

__– 2x__;

__3y__and

__-y.__

(3) The pairs of like terms are:

__2ab__and

__– ab__;

__b__and

^{2}__3b__.

^{2 }**Solution 4:**

(1) m + 3 = 2 + 3 = 5

(2) 4m^{2} = 4 × (2 × 2) = 4 × 4 = 16

(3) m^{2} + 6 = (2 × 2) + 6 = 4 + 6 = 10

(4) 3n^{2 }= 3(1 × 1) = 3

(5) 5m – 6n = (5 × 2) – (6 × 1) = 10 – 6 = 4

(6) mn – n = (2 × 1) – 1 = 2 – 1 = 1

(7) n^{2} + 3mn = (1 × 1) + 3(2 × 1) = 1 + 6 = 7

(8) 2m – 3n^{2} = (2 × 2) – 3(1 × 1) = 4 – 3 = 1

(9) 3m^{2} – 12mn + 4n^{2}

= 3(2 × 2) – 12(2 × 1) + 4(1 × 1)

= 3(4) – 12(2) + 4

= 12 – 24 + 4

= 16 – 24

= (-8)

(10) 3n – 2m^{2} + 3

= 3(1) -2(2 × 2) + 3

= 3 – 2(4) + 3

= 3 – 8 + 3

= 6 – 2

= (-2)

**Practice – 1**

**Solution 1:**

(1) 7x^{3} + 8x^{2} + 9xy + 4y^{2}

There are 4 terms in the polynomial.

(2) 2xy + 3x^{2} – 25y^{3}

There are three terms in the polynomial.

(3) a^{2}bc

There is only on term in the polynomial.

(4) 6a + 5b – 10ab – a^{2} – b^{2}

There are five terms in the polynomial.

**Solution 2:**

Polynomials having different terms:

1) 6a + 5b – 10ab

2) 10ab – a^{2}bc

3) 2a^{2}b^{2}

4) 8ab^{4}c

5) 6a -3b

6) y^{2} + 2xy + 3x^{2}

**Solution 3:**

The polynomials written in question 2 can be classified into monomials, binomials and trinomials as follows:

**Practice – 2**

**Solution 1:**

The monomials from the list of given polynomials are as follows:

8ab, -9x^{2}, -7x^{2}y^{2}, 9abc

**Solution 2:**

The table below shows three illustrations each of monomial, binomial and trinomial:

**Practice – 3**

**Solution 1:**

**Solution 2:**

**Solution 3:**

(1) The coefficient of the term x^{2} is 1.

[x^{2 }= 1 × x^{2}]

(2) The power of the term 3abc is 3.

The power of the term 3abc is = 1 + 1 + 1 = 3

(3) The power of the term 7 in 12x + 7 is 0.

7 is the constant term and in a constant term, the power of the variable is zero.

7 = 7 × x^{0} …. (x^{0 }= 1)

**Practice – 4**

**Solution 1:**

The pairs of like terms are:

- 7x
^{2}and -5x^{2} - -3y
^{2}and -10y^{2} - 3a
^{2}b^{2}and 6a^{2}b^{2} - xy and 3xy

**Solution 2:**

The pairs of unlike terms are:

(1) 5x and 3xy

(2) -3y^{2} and -5x^{2}

(3) xy and 7ab

(4) -10y^{2} and 6a^{2}b^{2}

[Note: Many more pairs of unlike terms are possible in the given example.]

**Practice – 5**

**Solution 1:**

(1) x + y = 1 + 3 = 4

(2) x + y – a = 1 + 3 + 2 = 6

(3) 4x – y = 4 + 3 = 1

(4) a^{2} – x = (2 × 2) – 1 = 4 – 1 = 3

(5) x^{2 }= (x × x) = (1 × 1) = 1

(6) 3a + xy = (3 × 2) + (1 × 3) = 6 + 3 = 9

(7) y^{2} – a^{2} = (y × y) – (a × a) = (3 × 3) – (2 × 2) = 9 – 4 = 5

(8) x^{2} – 6xy + y^{2 }= (x × x) – 6 × x × y + (y × y)

= (1 × 1) – (6× 1 × 3) + (3 × 3)

= 1 – 18 + 9

= -8

(9) 4x^{2} + 2xy + 9y^{2 }= 4(x × x) + 2 × x × y + 9(y × y)

= 4(1 × 1) + (2 × 1 × 3) + 9(3 × 3)

= 4 + 6 + 81

= 91

(10) a^{2} – 6ax + 9x^{2}

= (a × a) – (6 × a × x) + 9(x × x)

= (2 × 2) – (6 × 2 × 1) + 9(1 × 1)

= 4 – 12 + 9

= 13 – 12 = 1