**Find and correct the errors in the following mathematical statements.**

**1. 4(x–5) = 4x–5**

**Solution:**

Let us take LHS

= 4(x- 5)

= 4x – 20 ≠ 4x – 5 = RHS

Hence, the correct statement is 4(x-5) = 4x–20

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

**Solution:**

Let us take LHS

= x(3x+2)

= 3x^{2}+2x ≠ 3×2+2 = RHS

Hence, the correct solution is x(3x+2) = 3x^{2}+2x

**3. 2x+3y = 5xy**

**Solution:**

Here,

LHS= 2x+3y

RHS = 5xy

Hence, LHS ≠ RHS

The correct statement is 2x+3y = 2x+3 y

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

**Solution:**

We take LHS:

LHS = x+2x+3x = 6x

Hence, LHS≠ RHS

The correct statement is x+2x+3x = 6x

**5. 5y+2y+y–7y = 0**

**Solution:**

We take LHS

LHS = 5y+2y+y–7y = y

LHS ≠ RHS

Hence, the correct statement is 5y+2y+y–7y = y

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

**Solution:**

We take LHS

LHS = 3x+2x = 5x

LHS ≠ RHS

Hence, the correct statement is 3x+2x = 5x

**7. (2x) ^{2}+4(2x)+7 = 2×2+8x+7**

**Solution:**

We take LHS

LHS = (2x)^{2}+4(2x)+7

= 4x^{2}+8x+7

LHS ≠ RHS

Hence, the correct statement is (2x)^{2}+4(2x)+7 = 4x^{2}+8x+7

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

**Solution:**

We take LHS

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

= 4x^{2}+5x ≠ 9x

LHS ≠ RHS

Hence, the correct statement is(2x)^{2}+5x = 4x^{2}+5x

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

**Solution:**

We take LHS

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

= (3x)^{2}+2^{2}+2x2x3x

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

LHS ≠ RHS

Hence, the correct statement is (3x + 2)^{2} = 9x^{2}+4+12x

**10. Substituting x = – 3 in**

**(a) x ^{2} + 5x + 4 gives (– 3) 2+5(– 3) +4 = 9+2+4 = 15**

**Solution:**

= (– 3) ^{2}+5(– 3) + 4

= 9–15+4

= – 2.

Hence, this is the correct answer.

**(b) x ^{2} – 5x + 4 gives (– 3) 2– 5( – 3)+4 = 9–15+4 = – 2**

**Solution:**

= (–3) 2–5(– 3) +4

= 9+15+4

= 28.

Hence, this is the correct answer

**(c) x ^{2} + 5x gives (– 3) 2+5(–3) = – 9–15 = – 24**

**Solution:**

= (– 3) 2+5(–3)

= 9–15

= -6.

Hence, this is the correct answer

**11.(y–3) ^{2} = y^{2}–9**

**Solution:**

LHS = (y–3)^{2}

Using identity: (a–b) ^{2} = a^{2}+b^{2}-2ab

(y – 3)^{2}

= y^{2}+(3)^{2}–2y×3

= y^{2}+9 –6y ≠ y^{2} – 9

LHS ≠ RHS

The correct statement is (y–3)^{2} = y^{2} + 9 – 6y

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

**Solution:**

LHS = (z+5)^{2}

Using identity: (a+b)^{2} = a^{2}+b^{2}+2ab.

(z+5)^{2} = z^{2}+5^{2}+2×5×z = z^{2}+25+10z ≠ z^{2}+25 = RHS

LHS ≠ RHS

The correct statement is (z+5)^{2} = z^{2}+25+10z

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

**Solution:**

LHS = (2a+3b) (a–b)

= 2a(a–b)+3b(a–b)

= 2a^{2}–2ab+3ab–3b^{2}

= 2a^{2}+ab–3b^{2} ≠ 2a^{2}–3b^{2}

LHS ≠ RHS

The correct statement is (2a +3b)(a –b) = 2a^{2}+ab–3b^{2}

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

**Solution:**

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

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

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

= a^{2}+6a+8

LHS ≠ RHS

Hence, the correct statement is (a+4)(a+2) = a^{2}+6a+8

**15. (a–4)(a–2) = a ^{2}–8**

**Solution:**

LHS = (a–4)(a–2)

= a(a–2)–4(a–2)

= a^{2}–2a–4a+8

= a^{2}–6a+8

LHS ≠ RHS

The correct statement is (a–4)(a–2) = a^{2}–6a+8

**16. 3x ^{2}/3x^{2} = 0**

Solution:

LHS = 3x^{2}/3x^{2} = 1

LHS ≠ RHS

The correct statement is 3x^{2}/3x^{2} = 1

**17. (3x ^{2}+1)/3x^{2} = 1 + 1 = 2**

**Solution:**

LHS = (3x^{2}+1)/3x^{2}

= (3x^{2}/3x^{2})+(1/3x^{2})

= 1+(1/3x^{2}) ≠ 2

LHS ≠ RHS

The correct statement is (3×2+1)/3×2 = 1+(1/3×2)

**18. 3x/(3x+2) = ½**

**Solution:**

LHS = 3x/(3x+2) ≠ 1/2

LHS ≠ RHS

The correct statement is 3x/(3x+2) = 3x/(3x+2)

**19. 3/(4x+3) = 1/4x**

**Solution:**

LHS = 3/(4x+3) ≠ 1/4x

LHS ≠ RHS

The correct statement is 3/(4x+3) = 3/(4x+3)

**20. (4x+5)/4x = 5**

**Solution:**

LHS = (4x+5)/4x

= 4x/4x + 5/4x

= 1 + 5/4x ≠ 5 = RHS

LHS ≠ RHS

The correct statement is (4x+5)/4x = 1 + (5/4x)

**21. (7x + 5)/5 = 7x**

**Solution:**

LHS = (7x+5)/5

= (7x/5)+ 5/5

= (7x/5)+1 ≠ 7x = RHS

LHS ≠ RHS

Hence, the correct statement is (7x+5)/5 = (7x/5) +1

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