Class 8 NCERT Solutions- Chapter 14 Factorisation – Exercise 14.4

Find and correct the errors in the following mathematical statements:

Question 1. 4(x – 5) = 4x – 5

Solution:

Given: 4(x – 5) = 4x – 5

Now we check if the given statement is correct or not

Taking L.H.S:

= 4(x – 5)

= 4x – 20

L.H.S ≠ R.H.S

So, the correct solution of 4(x – 5) = 4x – 20

Question 2. x(3x + 2) = 3x²+ 2

Solution:

Given: x(3x + 2) = 3x²+ 2

Now we check if the given statement is correct or not

Taking L.H.S:

= x(3x + 2)

= 3x² + 2x

L.H.S ≠ R.H.S

So, the correct solution of x(3x + 2) = 3x²+ 2x

Question 3. 2x + 3y = 5xy

Solution:

Given: 2x + 3y = 5xy

Here, L.H.S ≠ R.H.S

So, the correct solution of 2x + 3y = 2x + 3y

Question 4. x + 2x + 3x = 5x 

Solution:

Given: x + 2x + 3x = 5x 

Now we check if the given statement is correct or not

Taking L.H.S:

= x + 2x + 3x

= 6x

L.H.S ≠ R.H.S

So, the correct solution of x + 2x + 3x = 6x

Question 5. 5y + 2y + y – 7y = 0 

Solution:

Given: 5y + 2y + y – 7y = 0 

Now we check if the given statement is correct or not

Taking L.H.S:

= 5y + 2y + y – 7y 

= y

L.H.S ≠ R.H.S

So, the correct solution of 5y + 2y + y – 7y = y

Question 6. 3x + 2x = 5x²

Solution:

Given: 3x + 2x = 5x²

Now we check if the given statement is correct or not

Taking L.H.S:

= 3x + 2x

= 5x

L.H.S ≠ R.H.S

So, the correct solution of 3x + 2x = 5x

Question 7. (2x)²+ 4(2x) + 7 = 2x²+ 8x + 7 

Solution:

Given: (2x)²+ 4(2x) + 7 = 2x²+ 8x + 7 

Now we check if the given statement is correct or not

Taking L.H.S:

= (2x)²+ 4(2x) + 7

= 4x² + 8x + 7

L.H.S ≠ R.H.S

So, the correct solution of (2x)²+ 4(2x) + 7 = 4x² + 8x + 7

Question 8. (2x)²+ 5x = 4x + 5x = 9x

Solution:

Given: (2x)²+ 5x = 4x + 5x = 9x

Here, 

4x + 5x ≠ 9x

So, we check (2x)²+ 5x = 4x + 5x or not

Taking L.H.S:

= (2x)²+ 5x

= 4x² + 5x 

L.H.S ≠ R.H.S

So, the correct solution of (2x)²+ 5x = 4x² + 5x 

Question 9. (3x + 2)²= 3x²+ 6x + 4 

Solution:

Given: (3x + 2)²= 3x²+ 6x + 4 

Now we check if the given statement is correct or not

Taking L.H.S:

= (3x + 2)²

= 9x² + 6x + 4

L.H.S ≠ R.H.S

So, the correct solution of (3x + 2)² = 9x² + 6x + 4

Question 10. Substituting x = – 3 in

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

Solution:

Given: x²+ 5x + 4

Now substitute the value of x = -3 in the given equation, 

= (-3)²+ 5(-3) + 4

= 9 – 15 + 4

= -2

So the correct solution of x²+ 5x + 4 = -2

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

Solution:

Given: x² – 5x + 4

Now substitute the value of x = -3 in the given equation, 

= (-3)² – 5(-3) + 4

= 9 + 15 + 4

= 28

So the correct solution of x² – 5x + 4 = 28

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

Solution:

Given: x² + 5x 

Now substitute the value of x = -3 in the given equation, 

= (-3)² + 5(-3) 

= 9 – 15 

= -6

So the correct solution of x² + 5x = -6

Question 11. (y – 3)² = y² – 9 

Solution:

Given: (y – 3)² = y² – 9 

Now we check if the given statement is correct or not

Taking L.H.S:

= (y – 3)²

= y² – 6y + 9

L.H.S ≠ R.H.S

So, the correct solution of (y – 3)² = y² – 6y + 9

Question 12. (z + 5)² = z² + 25

Solution:

Given: (z + 5)² = z²+ 25

Now we check if the given statement is correct or not

Taking L.H.S:

= (z + 5)²

= z² + 10z + 25

L.H.S ≠ R.H.S

So, the correct solution of (z + 5)² = z² + 10z + 25

Question 13. (2a + 3b) (a – b) = 2a² – 3b²

Solution:

Given: (2a + 3b) (a – b) = 2a² – 3b²

Now we check if the given statement is correct or not

Taking L.H.S:

= (2a + 3b) (a – b) 

= 2a² – 2ab + 3ab – 3b² 

= 2a² – 3b² + ab 

L.H.S ≠ R.H.S

So, the correct solution of (2a + 3b) (a – b) = 2a² – 3b² + ab 

Question 14. (a + 4) (a + 2) = a² + 8

Solution:

Given: (a + 4) (a + 2) = a² + 8

Now we check if the given statement is correct or not

Taking L.H.S:

= (a + 4) (a + 2)

= a² + 2a + 4a + 8

= a² + 6a + 8

L.H.S ≠ R.H.S

So, the correct solution of (a + 4) (a + 2) = a² + 6a + 8

Question 15. (a – 4) (a – 2) = a² – 8

Solution:

Given: (a – 4) (a – 2) = a² – 8

Now we check if the given statement is correct or not

Taking L.H.S:

= (a – 4) (a – 2)

= a² – 2a – 4a + 8

= a² – 6a + 8

L.H.S ≠ R.H.S

So, the correct solution of (a – 4) (a – 2) = a² – 6a + 8

Question 16. 3x²/3x² = 0

Solution:

Given: 3x²/3x² = 0

Now we check if the given statement is correct or not

Taking L.H.S:

= 3x²/3x²

= 1

L.H.S ≠ R.H.S

So, the correct solution of 3x²/3x² = 1

Question 17. (3x² + 1)/(3x²) = 1 + 1 = 2

Solution:

Given: (3x² + 1)/(3x²) = 1 + 1 = 2

Now we check if the given statement is correct or not

Taking L.H.S:

= (3x² + 1)/(3x²)

= 3x²/(3x²) + 1/(3x²)

= 1 + 1/(3x²)

L.H.S ≠ R.H.S

So, the correct solution of (3x² + 1)/(3x²) = 1 + 1/(3x²)

Question 18. (3x)/(3x + 2) = 1/2

Solution:

Given: (3x)/(3x + 2) = 1/2

Here, L.H.S ≠ R.H.S

So, the correct solution of (3x)/(3x + 2) = (3x)/(3x + 2)

Question 19. 3/(4x + 3) = 1/4x

Solution:

Given: 3/(4x + 3) = 1/4x

Here, L.H.S ≠ R.H.S

So, the correct solution of 3/(4x + 3) = 3/(4x + 3) 

Question 20. (4x + 5)/(4x) = 5

Solution:

Given: (4x + 5)/(4x) = 5

Now we check if the given statement is correct or not

Taking L.H.S:

= (4x + 5)/(4x) 

= (4x/4x) + 5/4x)

= 1 + 5/4x

L.H.S ≠ R.H.S

So, the correct solution of (4x + 5)/(4x) = 1 + 5/4x

Question 21. (7x + 5)/5 = 7x

Solution:

Given: (7x + 5)/5 = 7x

Now we check if the given statement is correct or not

Taking L.H.S:

= (7x + 5)/5

= (7x/5) + 5/5)

= 7x/5 + 1

L.H.S ≠ R.H.S

So, the correct solution of (7x + 5)/5 = 7x/5 + 1