NCERT Solutions Class 8 Mathematics Factorisation Ex 14.4

Find and correct the errors in the following mathematical statements:

Question : 1. 4(𝓍 − 5) = 4𝓍 − 5

Answer :
L.H.S. = 4(𝓍 − 5) = 4𝓍 − 20 ≠ R.H.S.

Hence the correct mathmatical statement is 4(𝓍 − 5) = 4𝓍 − 20

Question : 2. 𝓍(3𝓍 + 2) = 3𝓍² + 2

𝓍(3𝓍 + 2) = 3𝓍² + 2&sxcr; ≠ R.H.S.

Hence the correct mathmatical statement is 𝓍(3𝓍 + 2) = 3𝓍² + 2&sxcr;

Answer :
L.H.S. = 4(𝓍 − 5) = 4𝓍 − 20 ≠ R.H.S.

Question : 3. 2𝓍 + 3y = 5𝓍y

Answer :
L.H.S. = 2𝓍 + 3y = 2𝓍 + 3y ≠ R.H.S.

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

Question : 4. 𝓍 + 2𝓍 + 3𝓍 = 5𝓍

Answer :
L.H.S. = 𝓍 + 2𝓍 + 3𝓍 = 6𝓍 ≠ R.H.S.

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

Question : 5. 5y + 2y + y − 7y = 0

Answer :
L.H.S. = 5y + 2y + y − 7y = 8y − 7y = y ≠ R.H.S.

Hence the correct mathmatical statement is 5y + 2y + y − 7y = y

Question : 6. 3𝓍 + 2𝓍 = 5𝓍²

Answer :
L.H.S. = 3𝓍 + 2𝓍 = 5𝓍 ≠ R.H.S.

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

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

Answer :
L.H.S. = (2𝓍)² + 4(2𝓍) + 7 = 4𝓍² + 8𝓍 + 7 ≠ R.H.S.

Hence the correct mathmatical statement is (2𝓍)² + 4(2𝓍) + 7 = 4𝓍² + 8𝓍 + 7

Question : 8. (2𝓍)² + 5𝓍 = 4𝓍 + 5𝓍 = 9𝓍

Answer :
L.H.S. = (2𝓍)² + 5𝓍 = 4𝓍² + 5𝓍 ≠ R.H.S.

Hence the correct mathmatical statement is (2𝓍)² + 5𝓍 = 4𝓍² + 5𝓍

Question : 9. (3𝓍 + 2)² = 3𝓍² + 6𝓍 + 4

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

= 9𝓍² + 12𝓍 + 4 ≠ R.H.S.

Hence the correct mathmatical statement is (3𝓍 + 2)² = 9𝓍² + 12𝓍 + 4

Question : 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

Answer :
(a) L.H.S. = 𝓍² + 5𝓍 + 4

Putting 𝓍 = −3 in given expression,

= (-3)² + 5(-3) + 4 = 9 – 15 + 4 = -2 ≠ R.H.S.

Hence 𝓍² + 5𝓍 + 4 gives −2



(b) L.H.S. = 𝓍² − 5𝓍 + 4

Putting 𝓍 = −3 in given expression,

(-3)² + 5(-3) + 4 = 9 + 15 + 4 = 28 ≠ R.H.S.

Hence 𝓍² + 5𝓍 + 4 gives 28.



(c) L.H.S. = 𝓍² + 5𝓍

Putting 𝓍 = −3 in given expression,

(-3)² + 5(-3) = 9 − 15 = −6 ≠ R.H.S

Hence 𝓍² + 5𝓍 gives −6.

Question : 11. (y – 3)² = y² − 9

Answer :
L.H.S. = (y – 3)² = y² −2 X y X 3 + 3² = y² − 6y + 9

[∵ (a – b)² = a² −2ab + b²]

= y² − 6y + 9 ≠ R.H.S.

Hence the correct statements is (y – 3)² = y² − 6y + 9

Question : 12. (z + 5)² = z² + 25

Answer :
L.H.S. = (z + 5)² = z² + 2 X z X 5 + 5² = z² + 10z + 25

[∵ (a + b)² = a² + 2ab + b²]

= z² + 10z + 25 ≠ R.H.S.

Hence the correct statements is (z + 5)² = z² + 10z + 25

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

Answer :
L.H.S. = (2a + 3b)(a – b) = (2a)(a – b) + (3b)(a – b) = 2a² − 2ab + 3ab − 3b²

= 2a² + ab − 3b² ≠ R.H.S.

Hence the correct statements is (2a + 3b)(a – b) = 2a² + ab − 3b²

Question : 14. (a + 4)(a + 2) = a² + 8

Answer :
L.H.S. = (a + 4)(a + 2) = a(a + 2) + 4(a + 2) = a² + 2a + 4a + 8²

= a² + 6a + 8 ≠ R.H.S.

Hence the correct statements is (a + 4)(a + 2) = a² + 6a + 8

Question : 15. (a − 4)(a − 2) = a² − 8

Answer :
L.H.S. = (a − 4)(a − 2) = a(a − 2) − 4(a − 2) = a² − 2a − 4a + 8²

= a² − 6a + 8 ≠ R.H.S.

Hence the correct statements is (a − 4)(a − 2) = a² − 6a + 8

Question : 16. ^3𝓍2⁄_{3𝓍² = 0}

Answer :