PSEB 8th Class Maths Solutions Chapter 14 Factorization Ex 14.4

Punjab State Board PSEB 8th Class Maths Book Solutions Chapter 14 Factorization Ex 14.4 Textbook Exercise Questions and Answers.

PSEB Solutions for Class 8 Maths Chapter 14 Factorization Ex 14.4

1. Find and correct the errors in the following mathematical statements:

Question 1.
4 (x – 5) = 4x – 5
Solution:
Error: 4 × – 5 = (- 20) and not (- 5)
Correct statement: 4 (x – 5) = 4x – 20

Question 2.
x (3x + 2) = 3x² + 2
Solution:
Error: x × 2 = 2x
Correct statement: x (3x + 2) = 3x² + 2x

Question 3.
2x + 3y = 5xy
Solution:
Error: 2x and 3y are unlike terms.
So their sum is not possible.
Correct statement: 2x + 3y = 2x + 3y

Question 4.
x + 2x + 3x = 5x
Solution:
Error: x, 2x and 3x are like terms. So sum of their coefficient =1 + 2 + 3 = 6.
Correct statement: x + 2x + 3x = 6x

Question 5.
5y + 2y + y – 7y = 0
Solution:
Error : 5y, 2y, y and – 7y all are like terms here. So sum of their coefficient = 5 + 2 + 1 – 7 = 1.
Correct statement: 5y + 2y + y – 7y = y

Question 6.
3x + 2x = 5x²
Solution:
Error: When like terms are added or subtracted their exponents do not change.
Correct statement: 3x + 2x = 5x

Question 7.
(2x)² + 4 (2x) + 7 = 2x² + 8x + 7
Solution:
Error: (2x)² = 2x × 2x = 4x²
Correct statement:
(2x)² + 4 (2x) + 7 = 4x² + 8x + 7

Question 8.
(2x)² + 5x = 4x + 5x = 9x
Solution:
Error : (2x)² = (2x × 2x) = 4x²
Correct statement: (2x)² + 5x = 4x² + 5x

Question 9.
(3x + 2)² = 3x² + 6x + 4
Solution:
Error : (3x + 2)²
= (3x)² + 2 (3x)(2) + (2)²
= 9x² + 12x + 4
Correct statement:
(3x + 2)² = 9x² + 12x + 4

10. Substituting x = – 3 in

Question (a)
x² + 5x + 4 gives (- 3)² + 5 (- 3) + 4 = 9 + 2 + 4 = 15
Solution:
Error : 5 (- 3) = – 15 and not 2
Correct statement:
Substituting x = (- 3) in, x² + 5x + 4
= (- 3)² + 5 (-3) + 4
= 9 – 15 + 4 = 9 + 4 – 15
= 13 – 15
= (-2)

Question (b)
x² – 5x + 4 gives (- 3)² – 5 (- 3) + 4 = 9 – 15 + 4 = -2
Solution:
Error: -5 (-3) = + 15 and not (-15)
Correct statement:
Substituting x = (- 3) in,
x² – 5x + 4
= (- 3)² – 5 (- 3) + 4
= 9 + 15 + 4
= 28

Question (c)
x² + 5x gives (- 3)² + 5 (- 3) = – 9 – 15 = – 24
Solution:
Error : (- 3)² = + 9
Correct statement:
Substituting x = (- 3) in, x² + 5x
= (- 3)² + 5 (- 3)
= 9 – 15 = – 6

Question 11.
(y – 3)² = y² – 9
Solution:
Error : (y – 3)²
= (y)² – 2 (y)(3) + (- 3)²
= y² – 6y + 9
Correct statement: (y – 3)² = y² – 6y + 9.

Question 12.
(z + 5)² = z² + 25
Solution:
Error : (z + 5)²
= (z)² + 2 (z)(5) + (5)²
= z² + 10 z + 25
Correct statement: (z + 5)²
= z² + 10z + 25

Question 13.
(2a + 3b) (a – b) = 2a² – 3b²
Solution:
Error : (2a + 3b) (a – b)
= 2a (a-b) + 3b (a-b)
= 2a² – 2ab + 3ab – 3b²
= 2a² + ab – 3b²
Correct statement: (2a + 3b) (a – b)
= 2a² + ab – 3b²

Question 14.
(a + 4) (a + 2) = a² + 8
Solution:
Error : (a + 4) (a + 2) = a (a + 2) + 4 (a + 2)
= a² + 2a + 4a + 8
= a² + 6a + 8
Correct statement: (a + 4) (a + 2)
= a² + 6a + 8

Question 15.
(a – 4) (a – 2) = a² – 8
Solution:
Error : (a – 4) (a – 2) = a (a – 2) – 4 (a – 2)
= a² – 2a – 4a + 8
= a² – 6a + 8
Correct statement: (a – 4) (a – 2)
= a² – 6a + 8

Question 16.
\(\frac{3 x^{2}}{3 x^{2}}\) = 0
Solution:
Error: Numerator and denominator, both are same. So their division is 1.
Correct statement:\(\frac{3 x^{2}}{3 x^{2}}\) = 1

Question 17.
\(\frac{3 x^{2}+1}{3 x^{2}}\) = 1 + 1 = 2
Solution:
Error: \(\frac{3 x^{2}+1}{3 x^{2}}=\frac{3 x^{2}}{3 x^{2}}+\frac{1}{3 x^{2}}\)
= 1 + \(\frac{1}{3 x^{2}}\)
Correct statement: \(\frac{3 x^{2}+1}{3 x^{2}}\) = 1 + \(\frac{1}{3 x^{2}}\)

Question 18.
\(\frac{3 x}{3 x+2}=\frac{1}{2}\)
Solution:
Error: Here, simplification of LHS is not possible.
Correct statement: \(\frac{3 x}{3 x+2}=\frac{3 x}{3 x+2}\)

Question 19.
\(\frac{3}{4 x+3}=\frac{1}{4 x}\)
Solution:
Error: Here, simplification of LHS is not possible.
Correct statement: \(\frac{3}{4 x+3}=\frac{3}{4 x+3}\)

Question 20.
\(\frac{4 x+5}{4 x}\) = 5
Solution:
Error: \(\frac{4 x+5}{4 x}\)
= \(\frac{4 x}{4 x}+\frac{5}{4 x}\)
= 1 + \(\frac{5}{4 x}\)
Correct statement: \(\frac{4 x+5}{4 x}\) = 1 + \(\frac{5}{4 x}\)

Question 21.
\(\frac{7 x+5}{5 x}\) = 7x
Error: \(\frac{7 x+5}{5 x}\)
= \(\frac{7 x}{5}+\frac{5}{5}\)
= \(\frac{7 x}{5}\) + 1
Correct statement: \(\frac{7 x+5}{5}=\frac{7 x}{5}\) + 1