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**EXERCISE 14.4 ****Question:** 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 + 4 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

**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 = 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) + 7 = 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} + 6x + 4

∴ The correct statement is:

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

x2 + 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

∴ The correct statement is

(z + 5)2 = z2 + 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

It is an incorrect statement.

∵ The correct statement is

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