Ncert Solutions For Class 8 Maths Ex 14.4

 Question 1:

Find the error in the following statement and correct it: 5(a – 4) = 5a – 4

sol.

L.H.S. = 5(a – 4) = 5a – 20 ≠ R.H.S.

Hence, the correct statement is 5a – 20.

Question 2:

Find the error in the following statement and correct it: a(3a + 2) = 3a² + 2

sol.

L.H.S. = a(3a + 2) = 3a² + 2a ≠ R.H.S.

Hence, the correct statement is a(3a + 2) = 3a² + 2a.

Question 3:

Find the error in the following statement and correct it: 2a + 3b = 5ab

sol.

L.H.S. = 2a + 3b ≠ R.H.S.

Hence, the correct statement is 2a + 3b = 2a + 3b.

 

Question 4:

Find the error in the following statement and correct it: a + 2a + 3a = 5a

sol.

L.H.S. = a + 2a + 3a = 6a ≠ R.H.S.

Hence, the correct statement is a + 2a + 3a = 6a.

 

Question 5:

Find the error in the following statement and correct it: 5b + 2b + b – 7b = 0

sol.

L.H.S. = 5b + 2b + b – 7b = b ≠ R.H.S.

Hence, the correct statement is 5b + 2b + b – 7b = b.

 

Question 6:

Find the error in the following statement and correct it: 3a + 2a = 5a²

sol.

L.H.S. = 3a + 2a = 5a ≠ R.H.S.

Hence, the correct statement is 3a + 2a = 5a.

 

Question 7:

Find the error in the following statement and correct it: (2a)² + 4(2a) + 7 = 2a² + 8a + 7

sol.

L.H.S. = (2a)² + 4(2a) + 7 = 4a² + 8a + 7 ≠ R.H.S.

Hence, the correct statement is (2a)² + 4(2a) + 7 = 4a² + 8a + 7.

 

Question 8:

Find the error in the following statement and correct it: (2a)² + 5a = 4a + 5a = 9a

sol.

L.H.S. = (2a)² + 5a = 4a² + 5a ≠ R.H.S.

Hence, the correct statement is (2a)² + 5a = 4a² + 5a.

 

Question 9:

Find the error in the following statement and correct it: (3a + 2)² = 3a² + 6a + 4

sol.

L.H.S. = (3a + 2)² = (3a)² + 2 x 3a x 2 + (2)² = 9a² + 12a + 4 ≠ R.H.S.

Hence, the correct statement is (3a + 2)² = 9a² + 12a + 4.

 

Question 10:

Find the error in the following statement and correct it:

Substituting a = -3 in:

i) a² + 5a + 4 gives 15

ii) a² – 5a + 4 gives -2

iii) a² + 5a = -24

sol.

i) L.H.S. = a² + 5a + 4

Substituting a= -3,

= (-3)² + 5(-3) + 4

= 9 – 15 + 4

= -2 ≠ R.H.S.

Hence, a² + 5a + 4 = -2.

 

ii) L.H.S. = a² – 5a + 4

Substituting a= -3,

= (-3)² – 5(-3) + 4

= 9 + 15 + 4

= 28 ≠ R.H.S.

Hence, a² – 5a + 4 = 28.

 

iii) L.H.S. =  a² + 5a

Substituting a= -3,

= (-3)² + 5(-3)

= 9 – 15

=-6 ≠ R.H.S.

Hence,  a² + 5a = -6.

 

Question 11:

Find the error in the following statement and correct it: (b – 3)² = b² – 9.

sol.

L.H.S. = (b – 3)² = b² – 2 x b x 3 + (3)² = b² – 6b + 9 ≠ R.H.S.

Hence, the correct statement is (b – 3)² = b² – 6b + 9.

 

 

Question 12:

Find the error in the following statement and correct it: (c + 5)² = c² +25.

sol.

L.H.S. = (c + 5)² = c² + 2 x c x 5 + (5)² = c² – 10b + 25 ≠ R.H.S.

Hence, the correct statement is (c + 5)² = c² – 10b + 25.

 

Question 13:

Find the error in the following statement and correct it: (2x + 3y)(x – y) = 2x² – 3y².

sol.

L.H.S. = (2x + 3y)(x – y) = 2x(x – y) + 3y(x – y)

= 2x² – 2ab + 3ab – 3b² = 2a² + ab – 3b² ≠ R.H.S.

Hence, the correct statement is (2x + 3y)(x – y) = 2a² + ab – 3b².

 

Question 14:

Find the error in the following statement and correct it: (x + 4)(x + 2) = x² + 8.

sol.

L.H.S. = (x + 4)(x + 2) = x(x +2) + 4(x + 2)

= x² + 2x + 4x + 8 = x² + 6x + 8 ≠ R.H.S.

Hence, the correct statement is (x + 4)(x + 2) = 2a² + x² + 6x + 8.

 

Question 15:

Find the error in the following statement and correct it: $\frac{3x^{2}}{3x^{2}}=0$

sol.

L.H.S. = $\frac{3x^{2}}{3x^{2}}=\frac{1}{1}=1$ ≠ R.H.S.

Hence, the correct statement is $\frac{3x^{2}}{3x^{2}}=1$.

 

 

Question 16:

Find the error in the following statement and correct it: $\frac{3x^{2}+1}{3x^{2}}=1+1=2$

sol.

L.H.S. = $\frac{3x^{2}+1}{3x^{2}}=\frac{3x^{2}}{3x^{2}}+\frac{1}{3x^{2}}=1+\frac{1}{3x^{2}}$ ≠ R.H.S.

Hence, the correct statement is $\frac{3x^{2}+1}{3x^{2}}=1+\frac{1}{3x^{2}}$.

 

Question 17:

Find the error in the following statement and correct it: $\frac{3x}{3x+2}=\frac{1}{2}$

sol.

L.H.S. = $\frac{3x}{3x+2}$ ≠ R.H.S.

Hence, the correct statement is $\frac{3x}{3x+2}=\frac{3x}{3x+2}$.

 

Question 18:

Find the error in the following statement and correct it: $\frac{3}{4x+3}=\frac{1}{4x}$

sol.

L.H.S. = $\frac{3}{4x+3}$ ≠ R.H.S.

Hence, the correct statement is $\frac{3}{4x+3}=\frac{3}{4x+3}$.

 

Question 19:

Find the error in the following statement and correct it: $\frac{4x+5}{4x}=5$

sol.

L.H.S. = $\frac{4x+5}{4x}=\frac{4x}{4x}+\frac{5}{4x}=1+\frac{5}{4x}$ ≠ R.H.S.

Hence, the correct statement is $\frac{4x+5}{4x}=1+\frac{5}{4x}$.

 

Question 20:

Find the error in the following statement and correct it: $\frac{7x+5}{5}=7x$

sol.

L.H.S. = $\frac{7x+5}{5}=\frac{7x}{5}+\frac{5}{5}=\frac{7x}{5}+1$ ≠ R.H.S.

Hence, the correct statement is $\frac{7x+5}{5}=\frac{7x}{5}+1$.

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