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Exercise 14.4 - Chapter 14 Factorisation class 8 ncert solutions Maths - SaraNextGen [2024]


Question 1:

Find and correct the errors in the statement: 4(x − 5) = 4x − 5

Answer:

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

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

Question 2:

Find and correct the errors in the statement: x(3x + 2) = 3x2 + 2

Answer:

L.H.S. = x(3x + 2) = x × 3x × 2 = 3x2 + 2x ≠ R.H.S.

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

Question 3:

Find and correct the errors in the statement: 2x + 3y = 5xy

Answer:

L.H.S = 2x + 3y ≠ R.H.S.

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

Question 4:

Find and correct the errors in the statement: x + 2x + 3x = 5x

Answer:

L.H.S = + 2x + 3x =1+ 2x + 3x = x(1 + 2 + 3) = 6≠ R.H.S.

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

Question 5:

Find and correct the errors in the statement: 5y + 2y + y − 7y = 0

Answer:

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

The correct statement is 5+ 2− 7y = y

Question 6:

Find and correct the errors in the statement: 3x + 2x = 5x2

Answer:

L.H.S. = 3x + 2x = 5x ≠ R.H.S

The correct statement is 3x + 2x = 5x

Question 7:

Find and correct the errors in the statement: (2x)2 + 4(2x) + 7 = 2x2 + 8x + 7

Answer:

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

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

Question 8:

Find and correct the errors in the statement: (2x)2 + 5x = 4x + 5x = 9x

Answer:

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

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

Question 9:

Find and correct the errors in the statement: (3x + 2)2 = 3x2 + 6x + 4

Answer:

L.H.S. = (3+ 2)2 = (3x)2 + 2(3x)(2) + (2)2 [(a + b)2 = a2 + 2ab + b2]

= 9x2 + 12x + 4 ≠ R.H.S

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

Question 10:

Find and correct the errors in the following mathematical statement. 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) For x = −3,

x2 + 5x + 4 = (−3)2 + 5 (−3) + 4 = 9 − 15 + 4 = 13 − 15 = −2

(b) For x = −3,

x2 − 5x + 4 = (−3)2 − 5 (−3) + 4 = 9 + 15 + 4 = 28

(c) For x = −3,

x2 + 5x = (−3)2 + 5(−3) = 9 − 15 = −6

Question 11:

Find and correct the errors in the statement: (y − 3)2 = y2 − 9

Answer:

L.H.S = (y − 3)2 = (y)2 − 2(y)(3) + (3)2 [(a − b)2 = a2 − 2ab + b2]

y2 − 6y + 9 ≠ R.H.S

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

Question 12:

Find and correct the errors in the statement: (z + 5)2 = z2 + 25

Answer:

L.H.S = (+ 5)2 = (z)2 + 2(z)(5) + (5)2 [(a + b)2 = a2 + 2ab + b2]

z2 + 10z + 25 ≠ R.H.S

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

Question 13:

Find and correct the errors in the statement: (2a + 3b) (a − b) = 2a2 − 3b2

Answer:

L.H.S. = (2a + 3b) (a − b) = 2a × a + 3b × a − 2a × b − 3b × b

= 2a2 + 3ab − 2ab − 3b2 = 2a2 + ab − 3b2 ≠ R.H.S.

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

Question 14:

Find and correct the errors in the statement: (a + 4) (a + 2) = a2 + 8

Answer:

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

a2 + 6+ 8 ≠ R.H.S

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

Question 15:

Find and correct the errors in the statement: (a − 4) (− 2) = a2 − 8

Answer:

L.H.S. = (a − 4) (a − 2) = (a)2 + [(− 4) + (− 2)] (a) + (− 4) (− 2)

a2 − 6a + 8 ≠ R.H.S.

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

Question 16:

Find and correct the errors in the statement: https://img-nm.mnimgs.com/img/study_content/curr/1/8/5/77/2927/Chapter%2014_html_m3b5161b.gif

Answer:

L.H.S = https://img-nm.mnimgs.com/img/study_content/curr/1/8/5/77/2927/Chapter%2014_html_m109779fb.gif

The correct statement is https://img-nm.mnimgs.com/img/study_content/curr/1/8/5/77/2927/Chapter%2014_html_757da67e.gif

Question 17:

Find and correct the errors in the statement: https://img-nm.mnimgs.com/img/study_content/curr/1/8/5/77/2929/Chapter%2014_html_m24d7d10f.gif

Answer:

https://img-nm.mnimgs.com/img/study_content/curr/1/8/5/77/2929/Chapter%2014_html_73042948.gif

The correct statement is https://img-nm.mnimgs.com/img/study_content/curr/1/8/5/77/2929/Chapter%2014_html_m218e312.gif

Question 18:

Find and correct the errors in the statement: https://img-nm.mnimgs.com/img/study_content/curr/1/8/5/77/2931/Chapter%2014_html_m450a53b1.gif

Answer:

L.H.S =https://img-nm.mnimgs.com/img/study_content/curr/1/8/5/77/2931/Chapter%2014_html_m46b35e06.gif

The correct statement is https://img-nm.mnimgs.com/img/study_content/curr/1/8/5/77/2931/Chapter%2014_html_m33c1af96.gif

Question 19:

Find and correct the errors in the statement: https://img-nm.mnimgs.com/img/study_content/curr/1/8/5/77/2932/Chapter%2014_html_7ab5e475.gif

Answer:

L.H.S. =https://img-nm.mnimgs.com/img/study_content/curr/1/8/5/77/2932/Chapter%2014_html_192fa8ee.gif  ≠ R.H.S.

The correct statement is https://img-nm.mnimgs.com/img/study_content/curr/1/8/5/77/2932/Chapter%2014_html_3702fc8c.gif

Question 20:

Find and correct the errors in the statement: https://img-nm.mnimgs.com/img/study_content/curr/1/8/5/77/2936/Chapter%2014_html_m58b7a8a.gif

Answer:

L.H.S. =https://img-nm.mnimgs.com/img/study_content/curr/1/8/5/77/2936/Chapter%2014_html_m157254e3.gif https://img-nm.mnimgs.com/img/study_content/curr/1/8/5/77/2936/Chapter%2014_html_1f80353b.gif

The correct statement is https://img-nm.mnimgs.com/img/study_content/curr/1/8/5/77/2936/Chapter%2014_html_m6f801ae.gif

Question 21:

Find and correct the errors in the statement: https://img-nm.mnimgs.com/img/study_content/curr/1/8/5/77/2938/Chapter%2014_html_508c1b38.gif

Answer:

L.H.S. =https://img-nm.mnimgs.com/img/study_content/curr/1/8/5/77/2938/Chapter%2014_html_3a541eb6.gif  https://img-nm.mnimgs.com/img/study_content/curr/1/8/5/77/2938/Chapter%2014_html_m3e037192.gif

The correct statement is https://img-nm.mnimgs.com/img/study_content/curr/1/8/5/77/2938/Chapter%2014_html_m4142eed2.gif

Also Read : Exercise-15.1-Chapter-15-Introduction-To-Graphs-class-8-ncert-solutions-Maths

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