**Download NCERT Solutions for Class 8 Maths Chapter 14 Exercise 14.4 – Factorisation**

**NCERT Solutions for Class 8 Maths ****Chapter 14 Exercise 14.4 – Factorisation****, has been designed by the NCERT to test the knowledge of the student on the topic – Finding the Error**

**Find and correct the errors in the following mathematical statements.**

**1. 4(x – 5) = 4x – 5**

**Sol.: **–

L.H.S. = 4(x – 5)

= 4×x – 4×5

= 4x – 20

≠ R.H.S.

Hence, the correct statement is 4(x – 5) = 4x – 20

**2. x(3x + 2) = 3x ^{2} + 2**

**Sol.: **–

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

= x×3x + x×2

= 3x^{2} +2x

≠ R.H.S.

Hence, the correct statement is x(3x + 2) = 3x^{2} +2x

**3. 2x + 3y = 5xy**

**Sol.: **–

L.H.S. = 2x + 3y

= 2x + 3y

≠ R.H.S.

Hence, the correct statement is 2x + 3y = 2x + 3y

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

**Sol.: **–

L.H.S. = x + 2x + 3x

= 1x + 2x + 3x

= 6x

≠ R.H.S.

Hence, the correct statement is x + 2x + 3x = 6x

**5. 5y + 2y + y – 7y = 0**

**Sol.: **–

L.H.S. = 5y + 2y + y – 7y

= 5y + 2y + 1y – 7y

= y

≠ R.H.S.

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

**6. 3x + 2x = 5x ^{2}**

**Sol.: **–

L.H.S. = 3x + 2x

= 5x

≠ R.H.S.

Hence, the correct statement is 3x + 2x = 5x

**7. (2x) ^{2} + 4(2x) + 7 = 2x^{2} + 8x + 7**

**Sol.: **–

L.H.S. = (2x)^{2} + 4(2x) + 7

= 4x^{2} + 8x +7

≠ R.H.S.

Hence, the correct statement is (2x)^{2} + 4(2x) + 7 = 4x^{2} + 8x +7

**8. (2x) ^{2} + 5x = 4x + 5x = 9x**

**Sol.: **–

L.H.S. = (2x)^{2} + 5x

= 4x^{2} + 5x

≠ R.H.S.

Hence, the correct statement is (2x)^{2} + 5x = 4x^{2} + 5x

**9. (3x + 2) ^{2} = 3x^{2} + 6x + 4**

**Sol.: **–

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

= 9x^{2} + 12x + 4

≠ R.H.S.

Hence, the correct statement is (3x + 2)^{2} = 9x^{2} + 12x + 4

**10. Substituting x = – 3 in**

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

**Sol.: **–

L.H.S. = *x*^{2} + 5*x *+ 4

For x = -3

= (-3)^{2} + 5 × (-3) + 4

= 9 – 15 + 4

= -2

≠ R.H.S.

Hence, the correct statement is ** x^{2} + 5x + 4 = -2** for x = -3.

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

**Sol.: **–

L.H.S. = x^{2} – 5x + 4

For x = -3

= (-3)^{2} -5 × (-3) + 4

= 9 + 15 + 4

= 28

≠ R.H.S.

Hence, the correct statement is **x ^{2} – 5x + 4= 28** for x = -3.

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

**Sol.: **–

L.H.S. = x^{2} + 5x

For x = -3

= (-3)^{2} + 5 × (-3)

= 9 – 15

= -6

≠ R.H.S.

Hence, the correct statement is **x ^{2} + 5x = -6** for x = -3.

**11. (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} – 2ab + b^{2} }

= y^{2} – 6y +9

≠ R.H.S.

Hence, the correct statement is (y – 3)^{2} = y^{2} – 6y +9

**12. (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} + 2ab + b^{2} }

= z^{2} + 10z + 25

≠ R.H.S.

Hence, the correct statement is (z + 5)^{2} = z^{2} + 10z + 25

**13. (2a + 3b) (a – b) = 2a ^{2} – 3b^{2}**

**Sol.: **–

L.H.S. = (2a + 3b) (a – b)

= 2a × a + 2a × (-b) + 3b × a + 3b × (-b)

= 2a^{2} – 2ab + 3ab – 3b^{2}

= 2a^{2} + ab – 3b^{2
}≠ R.H.S.

Hence, the correct statement is (2a + 3b) (a – b) = 2a^{2} + ab – 3b^{2}

**14. (a + 4) (a + 2) = a ^{2} + 8**

**Sol.: **–

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

= a × a + a × 2 + 4 × a + 4 × 2

= a^{2} + 2a + 4a + 8

= a^{2} + 6a + 8

≠ R.H.S.

Hence, the correct statement is (a + 4) (a + 2) = a^{2} + 6a + 8

**15. (a – 4) (a – 2) = a ^{2} – 8**

**Sol.: **–

L.H.S. = (a – 4) (a – 2)

= a × a + a × (-2) + (-4) × a + (-4) × (-2)

= a^{2} – 2a – 4a + 8 .. { (x + a)(x + b) = x^{2} + (a + b)x + ab }

= a^{2} – 6a + 8

≠ R.H.S.

Hence, the correct statement is (a – 4) (a – 2) = a^{2} – 6a + 8

**16. = 0**

**Sol.: **–

L.H.S. =

= 1

≠ R.H.S.

Hence, the correct statement is = 1

**17. = 1+1 = 2**

**Sol.: **–

L.H.S. =

= +

= 1 +

≠ R.H.S.

Hence, the correct statement is = 1 +

**18. = **

**Sol.: **–

L.H.S. =

≠ R.H.S.

Hence, the correct statement is =

**19. = **

**Sol.: **–

L.H.S. =

≠ R.H.S.

Hence, the correct statement is =

**20. = 5**

**Sol.: **–

L.H.S. =

= +

= 1 +

≠ R.H.S.

Hence, the correct statement is

**21. = 7x**

**Sol.: **–

L.H.S. =

= +

= + 1

≠ R.H.S.

Hence, the correct statement is = + 1.

**The next Exercise for** **NCERT Solutions for Class 8 Maths Chapter 15 Exercise 15.1 – Introduction to Graphs**** ****can be accessed by clicking here**

** Maths – NCERT Solutions Class 8**

**Download NCERT Solutions for Class 8 Maths Chapter 14 Exercise 14.4 – Factorisation**

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