Question

simplify 7x(4xy-5y²)3x(-6xy+15x²)-4x(-xy-2y³)​

Answer 1

Answer:

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

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