NCERT Solutions Class 8th Maths Chapter 14 Factorisation Exercise 14.4

NCERT Solutions Class 8th Maths Chapter 14 Factorisation Exercise 14.4

NCERT Solutions Class 8th Maths Chapter 14 Factorisation Exercise 14.4

?Chapter – 14?

✍Factorisation✍

?Exercise 14.4?

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) = 3×2+2
Solution: LHS = x(3x+2) = 3×2+2x ≠ 3×2+2 = RHS
The correct solution is x(3x+2) = 3×2+2x

3. 2x+3y = 5xy
Solution: LHS= 2x+3y ≠ R. H. S
The correct statement is 2x+3y = 2x+3 y

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 = 0
Solution: LHS = 5y+2y+y–7y = y ≠ RHS
The correct statement is 5y+2y+y–7y = y

6. 3x+2x = 5×2
Solution: LHS = 3x+2x = 5x ≠ RHS
The correct statement is 3x+2x = 5x

7. (2x) 2+4(2x)+7 = 2×2+8x+7
Solution: LHS = (2x) 2+4(2x)+7 = 4×2+8x+7 ≠ RHS
The correct statement is (2x) 2+4(2x)+7 = 4×2+8x+7

8. (2x) 2+5x = 4x+5x = 9x
Solution: LHS = (2x) 2+5x = 4×2+5x ≠ 9x = RHS
The correct statement is(2x) 2+5x = 4×2+5x

9. (3x + 2) 2 = 3×2+6x+4
Solution: LHS = (3x+2) 2 = (3x)2+22+2x2x3x = 9×2+4+12x ≠ RHS
The correct statement is (3x + 2) 2 = 9×2+4+12x

10. 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

Solution:

(a) 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.

(b) Substituting x = – 3 in x2–5x+4
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 answer

11.(y–3)2 = y2–9
Solution: LHS = (y–3)2 , which is similar to (a–b)2 identity, where (a–b) 2 = a2+b2-2ab.
(y – 3)2 = y2+(3) 2–2y×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 identity, where (a+b) 2 = a2+b2+2ab.
(z+5) 2 = z2+52+2×5×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+ab–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. 3×2/3×2 = 0
Solution: LHS = 3×2/3×2 = 1 ≠ 0 = RHS
The correct statement is 3×2/3×2 = 1

17. (3×2+1)/3×2 = 1 + 1 = 2
Solution:  LHS = (3×2+1)/3×2 = (3×2/3×2)+(1/3×2) = 1+(1/3×2) ≠ 2 = RHS
The correct statement is (3×2+1)/3×2 = 1+(1/3×2)

18. 3x/(3x+2) = ½
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