NCERT Solutions For Class 8 Math Chapter – 14 Factorisation Exercise – 14.4

Find the correct the errors in the following mathematical statements.

1. 4(x – 5) = 4x – 5

Solution:-

 

4(x – 5) = 4x – 20 ≠ 4x – 5 = RHS

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

 

2. X(3x + 2) = 3x²+2

Solution:-

 

LHS = X(3X + 2) = 3x² + 2x ≠ 3x² + 2 = RHS

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

 

3. 2x + 3y =  5xy

Solution:-

 

LHS = 2x + 3y ≠ RHS

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

 

4. X + 2x + 3x = 5x

Solution:-

 

LHS = x + 2x  3x = 6x ≠ RHS

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

 

5. 5y + 2y + y – 7y

Solution:-

 

LHS = 5y + 2y + y – 7y  = y ≠ RHS

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

 

6. 3x + 2x = 5x²

Solution:-

 

LHS = 3x + 2x = 5x ≠ RHS

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

 

7. (2x)² + 4(2x) + 7 = 2x² + 8x + 7

Solution:-

 

LHS = (2x)² + 4(2x) + 7 = 4x + 8x + 7 ≠ RHS

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

8. (2x)²+ 5x = 4x + 5x = 9x

Solution:-

 

LHS = (2x)² + 5x = 4x + 5x ≠ 9x  ≠ RHS

The correct statement is (2x)² + 5x = 4x² + 6x

 

9. (3x + 2)²= 3x² + 6x + 4

Solution:-

 

LHS = (3x +  2)² = (3x)² +  2² + 2 x 2 x 3x = 9x² + 4 + 12x ≠ RHS

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

 

10. Substituting x = -3 in

• X²+ 5x + 4 gives  (-3)² + 5(-3) + 4 = 9 + 2 + 4 = 15
• X²– 5x + 4 gives (-3)² – 5(-3) + 4 = 9 – 15 + 4 = -2
• X²+ 5x gives (-3)² + 5(-3) = -9 – 15 = -24

Solution:-

 

• Substituting x = -3 in x²+ 5x + 4 , we have

X² + 5x + 4 = (-3)² + 5(-3) + 4 = 9 – 15 + 4 = -2

This is the correct answer.

 

• Substituting x = -3 in x²+ 5x

X² – 5x + 4 = (-3)² +  5(-3) + 4 = 9 + 15 + 4 = 28

This is the correct answer

 

( c ) Substituting x = -3 in x² + 5x

X² + 5x = (-3)² + 5(-3) = 9 – 15 = -6

This is the correct answers

 

11. (y – 3) = y² – 9

Solution:-

 

LHS = (y – 3)² , which is similar to (a – b)²

Identify where (a – b)² = a² + b² – 2ab

(y – 3)² = y² – (3)² -2 x y x 3

= y² + 9 – 6y ≠ y² – 9 = RHS

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

 

12. (z + 5)²= z² + 25

Solution:-

 

LHS = (z + 5)² , which is similar to (a + b)²

Identify where (a + b)² = a²  + b² + 2ab

(z + 5)² = z²  + 5² + 2 x 5 x z

= z² + 25 + 10z ≠ z² + 25 = RHS

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

 

13. (2a + 3b)(a – b) = 2a²– 3b²

Solution:-

 

LHS = (2a + 3b)(a – b) = 2a(a – b) + 3b (a – b)

= 2a² – 2ab + 3ab – 3b²

= 2a² – 3b² = RHS

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

 

14. (a + 4)(a + 2) = a²+ 8

Solution:-

 

LHS = (a + 4)(a + 2) = a(a + 2) + 4(a + 2)

= a² + 2a + 4a + 8

= a² + 6a + 8 ≠ a² + 8 = RHS

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

 

15. (a – 4)(a -2) = a² – 8

Solution:-

 

LHS = (a – 4)(a – 2) = a(a – 2) -4(a – 2)

= a² – 2a – 4a + 8

= a² – 6a + 8 ≠ a² – 8 = RHS

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

 

16. 3x²/3x²= 0

Solution:-

 

LHS = 3x²/3x² = 1 ≠ 0 = RHS

The correct statement is 3x²/3x² = 1

 

17. (3x²+ 1)/3x² = 1+ 1 = 2

Solution:-

 

LHS = (3x² + 1)/3x² = (3x²/3x²) + (1/3x²) = 1 + (1/3x²) ≠2  = RHS

The correct statement is (3x² + 1)/3x² = 1+ (1/3x²)

 

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

Solution:-

 

LHS = 3x/(3x + 2) ≠ 1/2 = RHS

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

 

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

Solution:-

 

LHS = 3/(4x + 3) ≠ 1/4x

The correct statement is 3/(4x + 3) = 3/(4x + 3)

 

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

Solution:-

 

LHS = (4x + 5)/4x = 4x/4x + 5/4x = 1 + 5/4x ≠ 5 = RHS

The correct statement is (4x + 5)/4x = 1 + (5/4x)

 

21. 7x + 5/5 = 7x

Solution:-

 

LHS = (7x + 5)/5 = (7x/5) + 5/5 = (7x/5) + 1 ≠ 7x = RHS

 

The correct statement is (7x + 5)/5 = (7x/5) + 1