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# 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.$$x + 2x + 3x = 5xy$$ 5. $$5y + 2y + y – 7y = 0$$ 6. $$3x + 2x = 5x^2$$ 7. $$(2x)^2 + 4(2x) + 7 = 2x^2 + 8x + 7$$ 8. $$(2x)^2 + 5x = 4x + 5x = 9x$$ 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. $$\frac { 3{ x }^{ 2 } }{ 3{ x }^{ 2 } } =0$$ 17. $$\frac { 3{ x }^{ 2 }+1 }{ 3{ x }^{ 2 } } =1+1=2$$ 18.$$\frac { 3x }{ 3x+2 } =\frac { 1 }{ 2 }$$ 19.$$\frac { 3 }{ 4x+3 } =\frac { 1 }{ 4x }$$ 20. $$\frac { 4x+5 }{ 4x } =5$$ 21. $$\frac { 7x+5 }{ 5 } =7x$$

1. We have LHS=$$4(x-5)=4\times x -4 \times 5 =4x-20$$

We should have RHS=LHS

Therefore,$$4(x-5)=4x-20$$ is the correct statement.

2. We have LHS=$$x(3x + 2)=x \times 3x + x \times 2 =3x^2+2x$$

We should have RHS=LHS

Therefore,$$x(3x + 2)=3x^2+2x$$ is the correct statement.

3.The given statement is incorrect only liked terms can be grouped together.Therefore, 2x+3y=2x+3y may be the correct statement

4.Using distributive property of multiplivation over addition:

$$LHS=x+2x+3x=6x\neq$$ given RHS

So x+2x+3x=6x is the correct statement

5.Using distributive property of multiplivation over addition:

$$LHS=5y+2y+y-7y=(8-7)y=7y\neq$$ given RHS

So 5y+2y+y-7y=7y is the correct statement

6.Using distributive property of multiplivation over addition:

$$LHS=3x + 2x=5x\neq$$ given RHS

So 3x + 2x=5x is the correct statement

7.We have LHS:$$(2x)^2 + 4(2x) + 7$$

$$=(2)^2\times (x)^2 + 4(2x) + 7= 4x^2 + 8x + 7\neq$$ given RHS

So $$(2x)^2 + 4(2x) + 7= 4x^2 + 8x + 7$$ is the correct statement

8.We have LHS:$$(2x)^2 + 5x$$

$$=(2)^2\times (x)^2 +5x= 4x^2 + 5x\neq$$ given every value in RHS

So $$(2x)^2 + 5x= 4x^2 +5x$$ is the correct statement

9.We have LHS:$$(3x + 2)^2$$

$$=(3x)^2+2\times (3x)\times(2)+2^2)=9x^2 +12x + 4\neq$$ given RHS

So $$(3x + 2)^2= 9x^2 +12x + 4$$ is the correct statement

10.(a)Substituting x=-3 in $$x^2 +5x + 4$$

$$=(-3)^2+5(-3)+4=9-15+4=-2 \neq$$ given RHS

So for x=-3, the value of $$x^2 +12x + 4 =-2$$

(b)Substituting x=-3 in $$x^2 -5x + 4$$

$$=(-3)^2-5(-3)+4=9+15+4=28 \neq$$ given RHS

So for x=-3, the value of $$x^2 -5x + 4 =28$$

(c)Substituting x=-3 in $$x^2 +5x$$

$$=(-3)^2+5(-3)=9-15=-6 \neq$$ given RHS

So for x=-3, the value of $$9x^2 +5x =62$$

11.We have, We have LHS:$$(y-3)^2$$

$$=(y)^2-2\times (y)\times(3)+3^2)=y^2 -6y + 9\neq$$ given RHS

So $$(y-3)^2= y^2 -6y + 9$$ is the correct statement

12.We have, We have LHS:$$(z+5)^2$$

$$=(z)^2+2\times (z)\times(5)+5^2)=z^2 +10z + 25\neq$$ given RHS

So $$(z+5)^2= z^2 +10z + 25$$ is the correct statement

13. Here we have LHS=$$(2a+3b)(a-b)$$

$$=2a(a-b)+3b(a-b)=2a \times a - 2a times b+3b \times a - 3a \times b$$

$$=2a^2+ab-3b^2\neq$$ given RHS

So $$(2a+3b)(a-b)=2a^2+ab-3b^2$$ is the correct statement

14.Here we have LHS=$$(a+4)(a+2)$$

$$=a(a+2)+4(a+2)=a \times a + a times 2+4 \times a + 4 \times 2$$

$$=a^2+6a+8\neq$$ given RHS

So $$(a+4)(a+2)=a^2+6a+8$$ is the correct statement

15.Here we have LHS=$$(a-4)(a-2)$$

$$=a(a-2)-4(a-2)=a \times a - a \times 2-4 \times a + 4 \times 2$$

$$=a^2-6a+8\neq$$ given RHS

So $$(a-4)(a-2)=a^2-6a+8$$ is the correct statement

16.We have LHS=$$\frac{3x^2}{3x^2}=1 \neq$$ given RHS

So we have $$\frac{3x^2}{3x^2}=1$$ as the correct statement

17.We have LHS=$$\frac{3x^2+1}{3x^2}=\frac{3x^2}{3x^2}+\frac{1}{3x^2}=1+\frac{1}{3x^2} \neq$$ given RHS

So we have $$\frac{3x^2+1}{3x^2}=1+\frac{1}{3x^2}$$ as the correct statement

18.We have LHS=$$\frac{3x}{3x+2}\neq \frac{1}2$$

So we have $$\frac{3x^2}{3x^2}=\frac{3x}{3x+2}$$ as the correct statement

19.Clearly in LHS we can see that, $$\frac{3}{4x+3} \neq \frac{1}{4x}$$

So we have $$\frac{3}{4x+3}=\frac{3}{4x+3}$$ as the correct statement

20.Clearly in LHS we can see that, $$\frac{4x+5}{4x}=\frac{4x}{4x}+\frac{5}{4x}=1+\frac{5}{4x} \neq 5$$

So we have $$\frac{4x+5}{4x}=1+\frac{5}{4x}$$ as the correct statement

21.Clearly in LHS we can see that, $$\frac{7x+5}{5}=\frac{7x}{5}+\frac{5}{5}=1+\frac{7x}{5} \neq 7x$$

So we have $$\frac{7x+5}{5}=1+\frac{7x}{5}$$ as the correct statement