# Exercise 14.4

Question 1

Find and correct the errors in the statement: 4(x − 5) = 4x − 5

Sol :

L.H.S. = 4(x − 5) = 4 × x − 4 × 5 = 4x − 20 ≠ R.H.S.

The correct statement is 4(x − 5) = 4x − 20

Question 2

Find and correct the errors in the statement: x(3x + 2) = 3x2 + 2

Sol :

L.H.S. = x(3x + 2) = x × 3x + x × 2 = 3x2 + 2x ≠ R.H.S.

The correct statement is x(3x + 2) = 3x2 + 2x

Question 3

Find and correct the errors in the statement: 2x + 3y = 5xy

Sol :

L.H.S = 2x + 3y ≠ R.H.S.

The correct statement is 2x + 3y = 2x + 3y

Question 4

Find and correct the errors in the statement: x + 2x + 3x = 5x

Sol :

L.H.S = x + 2x + 3x =1x + 2x + 3x = x(1 + 2 + 3) = 6x ≠ R.H.S.

The correct statement is x + 2x + 3x = 6x

Question 5

Find and correct the errors in the statement: 5y + 2y + y − 7y = 0

Sol :

L.H.S. = 5y + 2y + y − 7y = 8y − 7y = y ≠ R.H.S

The correct statement is 5y + 2y + y − 7y = y

Question 6

Find and correct the errors in the statement: 3x + 2x = 5x2

Sol :

L.H.S. = 3x + 2x = 5x ≠ R.H.S

The correct statement is 3x + 2x = 5x

Question 7

Find and correct the errors in the statement: (2x)2 + 4(2x) + 7 = 2x2 + 8x + 7

Sol :

L.H.S = (2x)2 + 4(2x) + 7 = 4x2 + 8x + 7 ≠ R.H.S

The correct statement is (2x)2 + 4(2x) + 7 = 4x2 + 8x + 7

Question 8

Find and correct the errors in the statement: (2x)2 + 5x = 4x + 5x = 9x

Sol :

L.H.S = (2x)2 + 5x = 4x2 + 5x ≠ R.H.S.

The correct statement is (2x)2 + 5x = 4x2 + 5x

Question 9

Find and correct the errors in the statement: (3x + 2)2 = 3x2 + 6x + 4

Sol :

L.H.S. = (3x + 2)2 = (3x)2 + 2(3x)(2) + (2)2 [(a + b)2 = a2 + 2ab + b2]

= 9x2 + 12x + 4 ≠ R.H.S

The correct statement is (3x + 2)2 = 9x2 + 12x + 4

Question 10

Find and correct the errors in the following mathematical statement. Substituting x = −3 in

(a) x2 + 5x + 4 gives (−3)2 + 5 (−3) + 4 = 9 + 2 + 4 = 15

(b) x2 − 5x + 4 gives (−3)2 − 5 (−3) + 4 = 9 − 15 + 4 = −2

(c) x2 + 5x gives (−3)2 + 5 (−3) = −9 − 15 = −24

Sol :

(a) For x = −3,

x2 + 5x + 4 = (−3)2 + 5 (−3) + 4 = 9 − 15 + 4 = 13 − 15 = −2

(b) For x = −3,

x2 − 5x + 4 = (−3)2 − 5 (−3) + 4 = 9 + 15 + 4 = 28

(c) For x = −3,

x2 + 5x = (−3)2 + 5(−3) = 9 − 15 = −6

Question 11

Find and correct the errors in the statement: (y − 3)2 = y2 − 9

Sol :

L.H.S = (y − 3)2 = (y)2 − 2(y)(3) + (3)2 [(ab)2 = a2 − 2ab + b2]

= y2 − 6y + 9 ≠ R.H.S

The correct statement is (y − 3)2 = y2 − 6y + 9

Question 12

Find and correct the errors in the statement: (z + 5)2 = z2 + 25

Sol :

L.H.S = (z + 5)2 = (z)2 + 2(z)(5) + (5)2 [(a + b)2 = a2 + 2ab + b2]

= z2 + 10z + 25 ≠ R.H.S

The correct statement is (z + 5)2 = z2 + 10z + 25

Question 13

Find and correct the errors in the statement: (2a + 3b) (ab) = 2a2 − 3b2

Sol :

L.H.S. = (2a + 3b) (ab) = 2a × a + 3b × a − 2a × b − 3b × b

= 2a2 + 3ab − 2ab − 3b2 = 2a2 + ab − 3b2 ≠ R.H.S.

The correct statement is (2a + 3b) (ab) = 2a2 + ab − 3b2

Question 14

Find and correct the errors in the statement: (a + 4) (a + 2) = a2 + 8

Sol :

L.H.S. = (a + 4) (a + 2) = (a)2 + (4 + 2) (a) + 4 × 2

= a2 + 6a + 8 ≠ R.H.S

The correct statement is (a + 4) (a + 2) = a2 + 6a + 8

Question 15

Find and correct the errors in the statement: (a − 4) (a − 2) = a2 − 8

Sol :

L.H.S. = (a − 4) (a − 2) = (a)2 + [(− 4) + (− 2)] (a) + (− 4) (− 2)

= a2 − 6a + 8 ≠ R.H.S.

The correct statement is (a − 4) (a − 2) = a2 − 6a + 8

Question 16

Find and correct the errors in the statement:

Sol :

L.H.S =

The correct statement is

Question 17

Find and correct the errors in the statement:

Sol :

The correct statement is

Question 18

Find and correct the errors in the statement:

Sol :

L.H.S =

The correct statement is

Question 19

Find and correct the errors in the statement:

Sol :

L.H.S. = ≠ R.H.S.

The correct statement is

Question 20

Find and correct the errors in the statement:

Sol :

L.H.S. =

The correct statement is

Question 21

Find and correct the errors in the statement:

Sol :

L.H.S. =

The correct statement is

Insert math as
$${}$$