RD Sharma Solutions (Part - 3) - Ex - 7.2, Algebraic Expressions, Class 7, Math | RD Sharma Solutions for Class 7 Mathematics PDF Download

QUESTION 14:

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

ANSWER 14:

Required expression = {(3x² - 5x + 2) + (- 5x² - 8x + 9)} - (4x² - 7x + 9)
                                  = {3x² - 5x + 2 - 5x² - 8x + 9} -  (4x² - 7x + 9)
                                  = {3x² - 5x² - 5x - 8x + 2 + 9} -  (4x² - 7x + 9)
                                  = {- 2x² - 13x +11} - (4x² - 7x + 9)
                                  = - 2x² - 13x + 11 - 4x² + 7x - 9
                                  = - 2x² - 4x² - 13x + 7x + 11 - 9
                                  = - 6x² - 6x + 2

QUESTION 15:

Subtract the sum of 13x − 4y + 7z and −6z + 6x + 3y from the sum of 6x − 4y − 4z and 2x + 4y − 7.

ANSWER 15:

Sum of (13x - 4y + 7z) and ( - 6z + 6x + 3y)
= {(13x - 4y + 7z) + (- 6z + 6x + 3y)
={13x - 4y + 7z - 6z + 6x + 3y}
= {13x + 6x - 4y + 3y + 7z - 6z}
= 19x - y + z

Sum of (6x − 4y − 4z) and (2x + 4y − 7)
= (6x − 4y − 4z) + (2x + 4y − 7)
= 6x − 4y − 4z + 2x + 4y − 7
= 8x - 4z - 7

Now, required expression = {(8x - 4z - 7) - (19x - y + z)}
                                  = 8x - 4z - 7 - 19x + y - z
                                  = 8x - 19x + y - 4z - z - 7
                                  = - 11x + y - 5z - 7

QUESTION 16:

From the sum of x² + 3y² − 6xy, 2x² − y² + 8xy, y² + 8 and x² − 3xy subtract −3x² + 4y² − xy + x − y + 3.

ANSWER 16:

Sum of (x² + 3y² - 6xy), (2x² - y² + 8xy), (y² + 8) and (x² - 3xy)
={(x² + 3y² - 6xy) + (2x² - y² + 8xy) + ( y² + 8) + (x² - 3xy)}
={x² + 3y² - 6xy + 2x² - y² + 8xy + y² + 8 + x² - 3xy}
= {x²+ 2x²+ x² + 3y²- y² + y²- 6xy + 8xy - 3xy + 8}
= 4x² + 3y² - xy + 8

Now, required expression = (4x² + 3y² - xy + 8) - (- 3x² + 4y² - xy + x - y + 3)
                                  = 4x² + 3y² - xy + 8 + 3x² - 4y² + xy - x + y - 3
                                  = 4x² + 3x²+ 3y²- 4y²- x + y - 3 + 8
                                  = 7x² - y²- x + y + 5

QUESTION 17:

What should be added to xy − 3yz + 4zx to get 4xy − 3zx + 4yz + 7?

ANSWER 17:

The required expression can be got by subtracting xy - 3yz + 4zx from 4xy - 3zx + 4yz + 7.
Therefore, required expression = (4xy - 3zx + 4yz + 7) - (xy - 3yz + 4zx)
                                  = 4xy - 3zx + 4yz + 7 - xy + 3yz - 4zx
                                  = 4xy - xy - 3zx - 4zx + 4yz + 3yz + 7
                                  = 3xy - 7zx + 7yz + 7

QUESTION 18:

What should be subtracted from x² − xy + y² −x + y + 3 to obtain −x² + 3y² − 4xy + 1?

ANSWER 18:

Let 'M' be the required expression. Then, we have
x² - xy + y² - x + y + 3 - M = - x² + 3y² - 4xy + 1
Therefore,
M = (x² - xy + y² - x + y + 3) - (- x² + 3y² - 4xy + 1)
    = x² - xy + y² - x + y + 3 + x² - 3y² + 4xy - 1
Collecting positive and negative like terms together, we get
x² + x²- xy + 4xy + y²- 3y² - x + y + 3 - 1
= 2x² + 3xy- 2y²- x + y + 2

QUESTION 19:

How much is x − 2y + 3z greater than 3x + 5y − 7?

ANSWER 19:

Required expression  = (x - 2y + 3z) - (3x + 5y - 7)
                                   =  x - 2y + 3z - 3x - 5y + 7
Collecting positive and negative like terms together, we get
x - 3x - 2y - 5y + 3z + 7
= - 2x - 7y + 3z + 7

QUESTION 20:

How much is x² − 2xy + 3y² less than 2x² − 3y² + xy?

ANSWER 20:

Required expression = (2x² - 3y² + xy) - (x² - 2xy + 3y²)
                                  = 2x² - 3y² + xy - x² + 2xy - 3y²
Collecting positive and negative like terms together, we get
2x² - x² - 3y² - 3y² + xy + 2xy
 = x² - 6y² + 3xy

QUESTION 21:

How much does a² − 3ab + 2b² exceed 2a² − 7ab + 9b²?

ANSWER 21:

Required expression = (a² - 3ab + 2b²) - (2a² - 7ab + 9b²)
                                  = a² - 3ab + 2b² - 2a² + 7ab - 9b²
Collecting positive and negative like terms together, we get
                                  =  a² - 2a²  - 3ab + 7ab  + 2b² -  9b² 
                                  = - a² + 4ab - 7b²

QUESTION 22:

What must be added to 12x³ − 4x² + 3x − 7 to make the sum x³ + 2x² − 3x + 2?

ANSWER 22:

Let 'M' be the required expression. Thus, we have
12x³ - 4x² + 3x - 7 + M = x³ + 2x² - 3x + 2
Therefore,
M = (x³ + 2x² - 3x + 2) - (12x³ - 4x² + 3x - 7)
    =  x³ + 2x² - 3x + 2 - 12x³ + 4x² - 3x + 7
Collecting positive and negative like terms together, we get
x³- 12x³ + 2x² + 4x² - 3x - 3x + 2 + 7
= - 11x³ + 6x² - 6x + 9

QUESTION 23:

If P = 7x² + 5xy − 9y², Q = 4y² − 3x² − 6xy and R = −4x² + xy + 5y², show that P + Q + R = 0.

ANSWER 23:

We have
P + Q + R = (7x² + 5xy - 9y²) + (4y² - 3x² - 6xy) + (- 4x² + xy + 5y²)
                 = 7x² + 5xy - 9y² + 4y² - 3x² - 6xy - 4x² + xy + 5y²
Collecting positive and negative like terms together, we get
7x²- 3x² - 4x² + 5xy - 6xy + xy - 9y² + 4y² + 5y²
= 7x²- 7x² + 6xy - 6xy  - 9y² + 9y² 
= 0

QUESTION 24:

If P = a² − b² + 2ab, Q = a² + 4b² − 6ab, R = b² + b, S = a² − 4ab and T = −2a² + b² − ab + a. Find P + Q + R + S − T.

ANSWER 24:

 We have
P + Q + R + S - T = {(a² - b² + 2ab) + (a² + 4b² - 6ab) + (b² + b) + (a² - 4ab)} - (-2a² + b² - ab + a)
                             = {a² - b² + 2ab + a² + 4b² - 6ab + b² + b + a² - 4ab}- (- 2a² + b² - ab + a)
                             = {3a² + 4b² - 8ab + b } - (-2a² + b² - ab + a)
                             = 3a²+ 4b² - 8ab + b + 2a² - b² + ab - a
Collecting positive and negative like terms together, we get
3a² + 2a² + 4b² - b² - 8ab + ab - a + b
= 5a² + 3b²- 7ab - a + b