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**EXERCISE 14.4 ****Question:** Find and correct the errors in the following mathematical statements.

1. 4(x â€“ 5) = 4x â€“ 5

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

3. 2x + 3y = 5xy

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

5. 5y + 2y + y â€“ 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 = â€“ 3 in

(a) x^{2} + 5x + 4 gives (â€“3)^{2} + 5(â€“3) + 4 = 9 + 2 + 4 = 15

(b) x^{2} â€“ 5x + 4 gives (â€“3)^{2} â€“ 5(â€“3) + 4 = 9 â€“ 15 + 4 = â€“ 2

(c) x^{2} + 5x + 4 gives (â€“3)^{2} + 5(â€“3) = â€“ 9 â€“ 15 = â€“ 24

11. (y â€“ 3)^{2} = y^{2 }â€“ 9

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

13. (2a + 3b)(a â€“ b) = 2a^{2} â€“ 3b^{2}

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

15. (a â€“ 4)(a â€“ 2) = a^{2} â€“ 8

**Solution:****1.** 4(x â€“ 5) = 4x â€“ 5

The given statement is incorrect.

The correct statement is:

4(x â€“ 5) = 4x â€“ 20 (âˆµ 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

âˆµ 1 + 2 + 3 = 5 is an incorrect statement.

âˆ´ The correct statement is:

x + 2x + 3x = 6x**5.** 5y + 2y + y â€“ 7y = 0

It is an incorrect statement.

âˆµ 5y + 2y + y = 8y and 8y â€“ 7y = y

âˆ´ The correct statement is

5y + 2y + y â€“ 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

âˆµ (2x)^{2} = 4x^{2}

âˆ´ 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.

âˆµ (2x)^{2} = 4x^{2}

âˆ´ The correct statement is:

(2x)^{2} + 5x = 4x^{2} + 5x**9. **(3x + 2)^{2}= 3x^{2} + 6x + 4

The given statement is incorrect.

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

= 9x^{2} + 6x + 4

âˆ´ The correct statement is:

(3x + 2)^{2} = 9x^{2} + 6x + 4**10.** (a) Incorrect statement.

âˆµ x^{2} + 5x + 4 = (â€“3)^{2} + 5(â€“3) + 4

= 9 â€“ 15 + 4

= (9 + 4) â€“ 15

= 13 â€“ 15 = â€“2

Thus, the correct statement is:

x^{2} + 5x + 4 = (â€“3)^{2} + 5(â€“3) + 4

= 9 â€“ 15 + 4 = â€“2

(b) We have

x^{2} â€“ 5x + 4 = (â€“3)^{2} â€“ 5(â€“3) + 4

= 9 + 15 + 4

= 28

âˆ´ The correct statement is

x^{2} â€“ 5x + 4 at x = â€“3 is

(â€“3)^{2} â€“ 5(â€“3) + 4 = 9 + 15 + 4 = 28

(c) âˆµ x^{2} + 5x at x = â€“ 3 is

(â€“3)^{2} + 5(â€“3) = 9 â€“ 15 = â€“6

âˆ´ The correct statement is

x2 + 5x at x = â€“3 is

(â€“3)2 + 5(â€“3) = 9 â€“ 15 = â€“6**11.** (y â€“ 3)^{2} = y^{2} â€“ 9

The given statement is incorrect.

âˆµ (y â€“ 3)^{2} = y^{2} â€“ 2(y)(3) + (3)^{2} = y^{2} â€“ 6y + 9

The correct statement is

(y â€“ 3)^{2} = y^{2} â€“ 6y + 9**12.** (z + 5)^{2} = z^{2} + 25

The given statement is incorrect.

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

= z^{2} + 10z + 25

âˆ´ The correct statement is

(z + 5)2 = z2 + 10z + 25**13.** (2a + 3b)(a â€“ b) = 2a^{2} â€“ 3b^{2}

âˆµ (2a + 3b) (a â€“ b) = a(2a + 3b) â€“ b (2a â€“ 3b)

= 2a^{2} + 3ab â€“ 2ab â€“ 3b^{2}

= 2a^{2} + ab â€“ 3b^{2}

âˆ´ The correct statement is

(2a + 3b)(a â€“ 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 â€“ 4)(a â€“ 2) = a^{2}â€“ 8

Since (a â€“ 4)(a â€“ 2) = a(a â€“ 2) â€“ 4(a â€“ 2)

= a^{2} â€“ 2a â€“ 4a + 8

= a^{2} â€“ 6a + 8

âˆ´ The correct statement is

(a â€“ 4)(a â€“ 2) = a^{2} â€“ 6a + 8

It is an incorrect statement.

âˆµ The correct statement is

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