Exercise 14.1 Exercise 14.2 Exercise 14.3 Exercise 14.4

# Exercise 14.4

Question 1

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

Sol :

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

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

Question 2

Find and correct the errors in the statement: *x*(3*x* + 2) = 3*x*^{2} + 2

Sol :

L.H.S. = *x*(3*x* + 2) = *x* × 3*x *+ *x* × 2 = 3*x*^{2} + 2*x* ≠ R.H.S.

The correct statement is *x*(3*x* + 2) = 3*x*^{2} + 2*x*

Question 3

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

Sol :

L.H.S = 2*x* + 3*y* ≠ R.H.S.

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

Question 4

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

Sol :

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

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

Question 5

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

Sol :

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

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

Question 6

Find and correct the errors in the statement: 3*x* + 2*x* = 5*x*^{2}

Sol :

L.H.S. = 3*x* + 2*x* = 5*x* ≠ R.H.S

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

Question 7

Find and correct the errors in the statement: (2*x*)^{2} + 4(2*x*) + 7 = 2*x*^{2} + 8*x* + 7

Sol :

L.H.S = (2*x*)^{2} + 4(2*x*) + 7 = 4*x*^{2} + 8*x* + 7 ≠ R.H.S

The correct statement is (2*x*)^{2} + 4(2*x*) + 7 = 4*x*^{2} + 8*x *+ 7

Question 8

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

Sol :

L.H.S = (2*x*)^{2} + 5*x* = 4*x*^{2} + 5*x* ≠ R.H.S.

The correct statement is (2*x*)^{2} + 5*x* = 4*x*^{2} + 5*x*

Question 9

Find and correct the errors in the statement: (3*x* + 2)^{2} = 3*x*^{2} + 6*x* + 4

Sol :

L.H.S. = (3*x *+ 2)^{2} = (3*x*)^{2} + 2(3*x*)(2) + (2)^{2} [(*a* + *b*)^{2} = *a*^{2} + 2*ab* + *b*^{2}]

= 9*x*^{2} + 12*x* + 4 ≠ R.H.S

The correct statement is (3*x* + 2)^{2} = 9*x*^{2} + 12*x* + 4

Question 10

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

(a) *x*^{2} + 5*x* + 4 gives (−3)^{2} + 5 (−3) + 4 = 9 + 2 + 4 = 15

(b) *x*^{2} − 5*x* + 4 gives (−3)^{2} − 5 (−3) + 4 = 9 − 15 + 4 = −2

(c) *x*^{2} + 5*x* gives (−3)^{2} + 5 (−3) = −9 − 15 = −24

Sol :

(a) For *x* = −3,

*x*^{2} + 5*x* + 4 = (−3)^{2} + 5 (−3) + 4 = 9 − 15 + 4 = 13 − 15 = −2

(b) For *x* = −3,

*x*^{2} − 5*x* + 4 = (−3)^{2} − 5 (−3) + 4 = 9 + 15 + 4 = 28

(c) For *x* = −3,

*x*^{2} + 5*x* = (−3)^{2} + 5(−3) = 9 − 15 = −6

Question 11

Find and correct the errors in the statement: (*y* − 3)^{2} = *y*^{2} − 9

Sol :

L.H.S = (*y* − 3)^{2} = (*y*)^{2} − 2(*y*)(3) + (3)^{2} [(*a* − *b*)^{2} = *a*^{2} − 2*ab* + *b*^{2}]

= *y*^{2} − 6*y* + 9 ≠ R.H.S

The correct statement is (*y* − 3)^{2} = *y*^{2} − 6*y* + 9

Question 12

Find and correct the errors in the statement: (*z* + 5)^{2} = *z*^{2} + 25

Sol :

L.H.S = (*z *+ 5)^{2} = (*z*)^{2} + 2(*z*)(5) + (5)^{2} [(*a* + *b*)^{2} = *a*^{2} + 2*ab* + *b*^{2}]

= *z*^{2} + 10*z* + 25 ≠ R.H.S

The correct statement is (*z *+ 5)^{2} = *z*^{2} + 10*z *+ 25

Question 13

Find and correct the errors in the statement: (2*a* + 3*b*) (*a* − *b*) = 2*a*^{2} − 3*b*^{2}

Sol :

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

= 2*a*^{2} + 3*ab* − 2*ab* − 3*b*^{2} = 2*a*^{2} + *ab* − 3*b*^{2} ≠ R.H.S.

The correct statement is (2*a* + 3*b*) (*a* − *b*) = 2*a*^{2} + *ab* − 3*b*^{2}

Question 14

Find and correct the errors in the statement: (*a* + 4) (*a* + 2) = *a*^{2} + 8

Sol :

L.H.S. = (*a* + 4) (*a* + 2) = (*a*)^{2} + (4 + 2) (*a*) + 4 × 2

= *a*^{2} + 6*a *+ 8 ≠ R.H.S

The correct statement is (*a* + 4) (*a* + 2) = *a*^{2} + 6*a *+ 8

Question 15

Find and correct the errors in the statement: (*a* − 4) (*a *− 2) = *a*^{2} − 8

Sol :

L.H.S. = (*a* − 4) (*a* − 2) = (*a*)^{2} + [(− 4) + (− 2)] (*a*) + (− 4) (− 2)

= *a*^{2} − 6*a* + 8 ≠ R.H.S.

The correct statement is (*a *− 4) (*a* − 2) = *a*^{2} − 6*a* + 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