Chapter 7: Algebraic Expressions Exercise – 7.2

Question: 1

Add the following:

(i) 3x and 7x

(ii) -5xy and 9xy

Solution:

We have

(i) 3x + 7x = (3 + 7) x = 10x

(ii) -5xy + 9xy = (-5 + 9)xy = 4xy

Question: 2

Simplify each of the following:

(i) 7x³y +9yx³

(ii) 12a²b + 3ba²

Solution:

Simplifying the given expressions, we have

(i) 7x³y + 9yx³ = (7 + 9)x³y = 16x³y

(ii) 12a²b + 3ba² = (12 + 3)a²b =15a²b

Question: 3

Add the following:

(i) 7abc, -5abc, 9abc, -8abc

(ii) 2x²y, - 4x²y, 6x²y, -5x²y

Solution:

Adding the given terms, we have

(i) 7abc + (-5abc) + (9abc) + (-8abc)

= 7abc – 5abc + 9abc – 8abc

= (7 – 5 + 9 – 8)abc

= (16 – 13)abc

= 3abc

(ii) 2x²y +(-4x²y) + (6x²y) + (-5x²y)

= 2x²y - 4x²y + 6x²y - 5x2y

= (2- 4 + 6 - 5) x 2y

= (8 - 9) x 2y

= -x²y

Question: 4

Add the following expressions:

(i) x³ -2x²y + 3xy²- y³, 2x³- 5xy² + 3x²y - 4y³

(ii) a⁴ - 2a³b + 3ab³ + 4a²b² + 3b⁴, - 2a⁴ - 5ab³ + 7a³b - 6a²b² + b⁴

Solution:

Adding the given expressions, we have

(i) x³ -2x²y + 3xy²- y³, 2x³- 5xy² + 3x²y - 4y³

Collecting positive and negative like terms together, we get

x³ +2x³ - 2x²y + 3x²y + 3xy² - 5xy² - y³- 4y³

= 3x³ + x²y - 2xy² - 5y³

(ii) a⁴ - 2a³b + 3ab³ + 4a²b² + 3b⁴, - 2a⁴ - 5ab³ + 7a³b - 6a²b² + b⁴

a⁴ - 2a³b + 3ab³ + 4a²b² + 3b⁴ - 2a⁴ - 5ab³ + 7a³b - 6a²b² + b⁴

Collecting positive and negative like terms together, we get

a⁴ - 2a⁴- 2a³b + 7a³b + 3ab³ - 5ab³ + 4a²b² - 6a²b² + 3b⁴ + b⁴

= - a⁴ + 5a³b - 2ab³ - 2a²b² + 4b⁴

Question: 5

Add the following expressions:

(i) 8a – 6ab + 5b, –6a – ab – 8b and –4a + 2ab + 3b

(ii) 5x³ + 7 + 6x - 5x², 2x² – 8 - 9x, 4x - 2x² + 3 x 3, 3 x 3 - 9x - x² and x - x² - x³ - 4

Solution:

(i) Required expression = (8a – 6ab + 5b) + (–6a – ab – 8b) + (–4a + 2ab + 3b)

Collecting positive and negative like terms together, we get

8a – 6a – 4a – 6ab – ab + 2ab + 5b – 8b + 3b

= 8a – 10a – 7ab + 2ab + 8b – 8b

= –2a – 5ab

(ii) Required expression = (5 x 3 + 7+ 6x - 5x²) + (2 x 2 – 8 - 9x) + (4x - 2x² + 3 x 3) + (3 x 3 - 9x-x²) + (x - x² - x³ - 4)

Collecting positive and negative like terms together, we get

5x³ + 3x³ + 3x³ - x³ - 5x² + 2x² - 2x²- x² - x² + 6x - 9x + 4x - 9x + x + 7 – 8 - 4

= 10x³ - 7x² - 7x - 5

Question: 6

Add the following:

(i) x – 3y – 2z

5x + 7y – 8z

3x – 2y + 5z

(ii) 4ab – 5bc + 7ca

–3ab + 2bc – 3ca

5ab – 3bc + 4ca

Solution:

(i) Required expression = (x – 3y – 2z) + (5x + 7y – 8z) + (3x – 2y + 5z)

Collecting positive and negative like terms together, we get

x + 5x + 3x – 3y + 7y – 2y – 2z – 8z + 5z

= 9x – 5y + 7y – 10z + 5z

= 9x + 2y – 5z

(ii) Required expression = (4ab – 5bc + 7ca) + (–3ab + 2bc – 3ca) + (5ab – 3bc + 4ca)

Collecting positive and negative like terms together, we get

4ab – 3ab + 5ab – 5bc + 2bc – 3bc + 7ca – 3ca + 4ca

= 9ab – 3ab – 8bc + 2bc + 11ca – 3ca

= 6ab – 6bc + 8ca

Question: 7

Add 2x² - 3x + 1 to the sum of 3x² - 2x and 3x + 7.

Solution:

Sum of 3x² - 2x and 3x + 7

= (3x² - 2x) + (3x +7)

=3x² - 2x + 3x + 7

= (3x² + x + 7)

Now, required expression = 2x² - 3x + 1+ (3x² + x + 7)

= 2x² + 3x² - 3x + x + 1 + 7

= 5x² - 2x + 8

Question: 8

Add x² + 2xy + y² to the sum of x² - 3y²and 2x² - y² + 9.

Solution:

Question: 9

Add a³+ b³ - 3 to the sum of 2a³ - 3b³ - 3ab + 7 and -a³ + b³ + 3ab - 9.

Solution:

Question: 10

Subtract:

(i) 7a²b from 3a²b

(ii) 4xy from -3xy

Solution:

(i) Required expression = 3a²b -7a²b

= (3 -7)a²b

= - 4a²b

(ii) Required expression = –3xy – 4xy

= –7xy

Question: 11

Subtract:

(i) - 4x from 3y

(ii) - 2x from – 5y

Solution:

(i) Required expression = (3y) – (–4x)

= 3y + 4x

(ii) Required expression = (-5y) – (–2x)

= –5y + 2x

Question: 12

Subtract:

(i) 6x³ −7x² + 5x − 3 from 4 − 5x + 6x² − 8x³

(ii) − x² −3z from 5x² – y + z + 7

(iii) x³ + 2x²y + 6xy² − y³ from y³−3xy²−4x²y

Solution:

Question: 13

From

(i) p3 – 4 + 3p², take away 5p² − 3p³ + p − 6

(ii) 7 + x − x², take away 9 + x + 3x² + 7x³

(iii) 1− 5y², take away y³ + 7y² + y + 1

(iv) x³ − 5x² + 3x + 1, take away 6x² − 4x³ + 5 + 3x

Solution:

Question: 14

From the sum of 3x² − 5x + 2 and − 5x² − 8x + 9 subtract 4x² − 7x + 9.

Solution:

You Might Like to Refer:

CBSE online class 10 | CBSE online class 12 |CBSE online coaching