GSEB Solutions Class 8 Maths Chapter 14 Factorization Ex 14.4

Gujarat Board GSEB Textbook Solutions Class 8 Maths Chapter 14 Factorization Ex 14.4 Textbook Questions and Answers.

Gujarat Board Textbook Solutions Class 8 Maths Chapter 14 Factorization Ex 14.4

Question 1.
Find and correct the errors in the following mathematical statements?
1. 4(x – 5) = 4x – 5
2. x(3x + 2) = 3x² + 2
3. 2x + 3y = 5xy
4. x + 2x + 3x = 5x
5. 5y + 2y + y – 7y = 0
6. 3x + 2x = 5x²
7. (2x)² + 4(2x) + 7 = 2x² + 8x + 7
8. (2x)² + 5x = 4x + 5x = 9x²
9. (3x + 2)² = 3x² + 6x + 4
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

11. (y – 3)² = y² – 9
12. (z + 5)² = z² + 25
13. (2a + 3b)(a – b) = 2a² – 3b²
14. (a + 4)(a + 2) = a² + 8
15. (a – 4)(a – 2) = a² – 8
16. \(\frac{3 x^{2}}{3 x^{2}}\)
17. \(\frac{3 x^{2}+1}{3 x^{2}}\)
18. \(\frac{3x}{3x+2}\) = \(\frac{1}{2}\)
19. \(\frac{3}{4x+3}\) = \(\frac{1}{4x}\)
20. \(\frac{4x+5}{4x}\) = 5
21. \(\frac{7x+5}{5}\) = 7x
Solution:
1. 4(x – 5) = 4x – 5
The given statement is incorrect.
The correct statement is:
4(x – 5) = 4x – 20 (∵4 × 5 = 20)

2. x(3x + 2) = 3x² + 2
It is an incorrect statement.
The correct statement is:
x(3x + 2) = 3x² + 2x

3. 2x + 3y = 5xy
It is an incorrect statement.
The correct statement is:
2x + 3y = 2x + 3y

4. x + 2x + 3x = 5x
∵ 1 + 2 + 3 = 5 is an incorrect statement.
∴ The correct statement is:
x + 2x + 3x = 6x

5. 5y + 2y + y – 7y = 0
It is an incorrect statement,
∵ 5y + 2y + y = 8y and 8y – 7y = y
∴ The correct statement is 5y + 2y + y – 7y = y

6. 3x + 2x = 5x²
It is an incorrect statement.
The correct statement is:
3x + 2x = 5x

7. (2x)² + 4(2x) + 7 = 2x² + 8x + 7
∵ (2x)² = 4x²
The given statement is incorrect.
The correct statement is:
(2x)² + 4(2x) + 1 = 4x² + 8x + 7

8. (2x)² + 5x = 4x + 5x = 9x, is an incorrect statement.
∵ (2x)² = 4x²
∴ The correct statement is:
(2x)² + 5x = 4x² + 5x

9. (3x + 2)² = 3x² + 6x + 4
The given statement is incorrect.
∵ (3x + 2)² = (3x)² + 2(3x)(2) + (2)²
= 9x² + 12x + 4
∴ The correct statement is:
(3x + 2)² = 9x² + 12x + 4

10. (a) Incorrect statement.
∵ x² + 5x + 4 = (-3)² + 5(-3) + 4
= 9 – 15 + 4
= (9 + 4) – 15
= 13 – 15 = – 2
Thus, the correct statement is:
x² + 5x + 4 = (-3)² + 5(-3) + 4
= 9 – 15 + 4 = -2

(b) We have
x² – 5x + 4 = (-3)² – 5(-3) + 4
= 9 + 15 + 4 = 28
∴ The correct statement is:
x² – 5x + 4 at x = -3 is
(-3)² – 5(-3) + 4 = 9 + 15 + 4 = 28

(c) ∵ x² + 5x at x = -3 is
(-3)² + 5(-3) = 9 – 15 = -6
∴ The correct statement is:
x² + 5x at x = -3 is
(-3)² + 5(-3) = 9 – 15 = -6

11. (y – 3)² = y² – 9
The given statement is incorrect
∵ (y – 3)² = y² – 2(y)(3) + (3)²
= y² – 6y + 9
The correct statement is
(y – 3)² = y² – 6y + 9

12. (z + 5)² = z² + 25
The given statement is incorrect
∵ (z + 5)² = z² + 2(z)(5) + (5)²
= z² + 10z + 25

13. (2a + 3b)(a – b) = 2a² – 3b²
∵ (2a + 3b) (a – b)
= a(2a + 3b) – b(2a + 3b)
= 2a² + 3ab – 2ab – 3b² = 2a² + ab – 3b²
∴ The correct statement is:
(2a + 3b)(a – b) = 2a² + ab – 3b²

14. (a + 4)(a + 2) = a² + 8
Since (a + 4) (a + 2)
= a(a + 4) + 2 (a + 4)
= a² + 4a + 2a + 8 = a² + 6a + 8

15. (b – 4)(a – 2) = a² – 8
Since(a – 4) (a – 2) = a(a – 2) – 4(a – 2)
= a² – 2a – 4a + 8 = a² – 6a + 8
∴ The correct statement is:
(a – 4)(a – 2) = a² – 6a + 8

16. \(\frac{3 x^{2}}{3 x^{2}}\) = 0
It is an incorrect statement
∵ The correct statement is
\(\frac{3 x^{2}}{3 x^{2}}\) = 1

17. \(\frac{3 x^{2}+1}{3 x^{2}}\) = 1 + 1 = 2
Since \(\frac{3 x^{2}+1}{3 x^{2}}=\frac{3 x^{2}}{3 x^{2}}+\frac{1}{3 x^{2}}\)
= 1 + \(\frac{1}{3 x^{2}}\)
∴ The correct statement is:
\(\frac{3 x^{2}+1}{3 x^{2}}=1+\frac{1}{3 x^{2}}\)

18. \(\frac{3}{3x+2}\) = \(\frac{1}{2}\)
The given statement is incorrect.
The correct statement is
\(\frac{3x}{3x+2}\) = \(\frac{3x}{3x+2}\)

19. \(\frac{3}{4x+3}\) = \(\frac{1}{4x}\)
The given statement is incorrect
The correct statement is
\(\frac{3}{4x+3}\) = \(\frac{3}{4x+3}\)

20. \(\frac{4x+5}{4x}\) = 5
∵ \(\frac{4x+5}{4x}\) = \(\frac{4x}{4x}\) + \(\frac{5}{4x}\) = 1 + \(\frac{5}{4x}\)
∴ The correct statement is:
\(\frac{7x+5}{5}\) = \(\frac{7x}{5}\) + 1