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) = 3x^{2} + 2

3. 2x + 3y = 5xy

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

5. 5y + 2y + y – 7y = 0

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

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

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

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

10. Substituting x = -3 in

(a) x^{2} + 5x + 4 gives (-3)^{2} + 5(-3) + 4

= 9 + 2 + 4 = 15

(b) x^{2} – 5x + 4 gives (-3)^{2} – 5(-3) + 4

= 9 – 15 + 4 = – 2

(c) x^{2} + 5x gives (-3)^{2} + 5(-3)

= – 9 – 15 = -24

11. (y – 3)^{2} = y^{2} – 9

12. (z + 5)^{2} = z^{2} + 25

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

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

15. (a – 4)(a – 2) = a^{2} – 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) = 3x^{2} + 2

It is an incorrect statement.

The correct statement is:

x(3x + 2) = 3x^{2} + 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 = 5x^{2}

It is an incorrect statement.

The correct statement is:

3x + 2x = 5x

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

∵ (2x)^{2} = 4x^{2}

The given statement is incorrect.

The correct statement is:

(2x)^{2} + 4(2x) + 1 = 4x^{2} + 8x + 7

8. (2x)^{2} + 5x = 4x + 5x = 9x, is an incorrect statement.

∵ (2x)^{2} = 4x^{2}

∴ The correct statement is:

(2x)^{2} + 5x = 4x^{2} + 5x

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

The given statement is incorrect.

∵ (3x + 2)^{2} = (3x)^{2} + 2(3x)(2) + (2)^{2}

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

∴ The correct statement is:

(3x + 2)^{2} = 9x^{2} + 12x + 4

10. (a) Incorrect statement.

∵ x^{2} + 5x + 4 = (-3)^{2} + 5(-3) + 4

= 9 – 15 + 4

= (9 + 4) – 15

= 13 – 15 = – 2

Thus, the correct statement is:

x^{2} + 5x + 4 = (-3)^{2} + 5(-3) + 4

= 9 – 15 + 4 = -2

(b) We have

x^{2} – 5x + 4 = (-3)^{2} – 5(-3) + 4

= 9 + 15 + 4 = 28

∴ The correct statement is:

x^{2} – 5x + 4 at x = -3 is

(-3)^{2} – 5(-3) + 4 = 9 + 15 + 4 = 28

(c) ∵ x^{2} + 5x at x = -3 is

(-3)^{2} + 5(-3) = 9 – 15 = -6

∴ The correct statement is:

x^{2} + 5x at x = -3 is

(-3)^{2} + 5(-3) = 9 – 15 = -6

11. (y – 3)^{2} = y^{2} – 9

The given statement is incorrect

∵ (y – 3)^{2} = y^{2} – 2(y)(3) + (3)^{2}

= y^{2} – 6y + 9

The correct statement is

(y – 3)^{2} = y^{2} – 6y + 9

12. (z + 5)^{2} = z^{2} + 25

The given statement is incorrect

∵ (z + 5)^{2} = z^{2} + 2(z)(5) + (5)^{2}

= z^{2} + 10z + 25

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

∵ (2a + 3b) (a – b)

= a(2a + 3b) – b(2a + 3b)

= 2a^{2} + 3ab – 2ab – 3b^{2} = 2a^{2} + ab – 3b^{2}

∴ The correct statement is:

(2a + 3b)(a – b) = 2a^{2} + ab – 3b^{2}

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

Since (a + 4) (a + 2)

= a(a + 4) + 2 (a + 4)

= a^{2} + 4a + 2a + 8 = a^{2} + 6a + 8

15. (b – 4)(a – 2) = a^{2} – 8

Since(a – 4) (a – 2) = a(a – 2) – 4(a – 2)

= a^{2} – 2a – 4a + 8 = a^{2} – 6a + 8

∴ The correct statement is:

(a – 4)(a – 2) = a^{2} – 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