Question : An example of an equality relation of two expressions in $x$. Which is not an identity, is:
Option 1: $(x+3)^{2}=x^{2}+6x+9$
Option 2: $(x+2y)^{3}=x^{3}+8y^{3}+6xy(x+2y)$
Option 3: $(x+2)^{2}=x^{2}+2x+4$
Option 4: $(x+3)(x–3)=x^{2}–9$
Correct Answer: $(x+2)^{2}=x^{2}+2x+4$
Solution : Given: $(x+3)^{2}=x^{2}+6x+9$ ⇒ $(x^{2}+9+6x)=x^{2}+6x+9$ Similarly, $(x+2y)^{3}=x^{3}+8y^{3}+6xy(x+2y)$ ⇒ $x^{3}+8y^{3}+6xy(x+2y)=x^{3}+8y^{3}+6xy(x+2y)$ Similarly, $(x+3)(x–3)=x^{2}-9$ Similarly, $(x+2)^{2}=x^{2}+2x+4$ ⇒ $(x^{2}+4+4x)=x^{2}+2x+4$ We can see this is not an identity. Hence, the correct answer is '$(x+2)^{2}=x^{2}+2x+4$'.
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Question : Simplify the given expression. $(x - 2y)(y - 3x) + (x + y)(x - y) + (x - 3y)(2x + y)$
Option 1: $2y(x - 3y)$
Option 2: $2y(x + 3y)$
Option 3: $2x(x - 3y)$
Option 4: $2x(x + 3y)$
Question : If $x^2+8 y^2+12 y-4 x y+9=0$, then the value of $(7 x+8 y)$ is:
Option 1: –33
Option 2: 9
Option 3: 33
Option 4: –9
Question : If $x^2+8 y^2-12 y-4 x y+9=0$, then the value of $(7x-8y)$ is:
Option 1: 21
Option 2: 5
Option 3: 12
Option 4: 9
Question : Simplify: $(x+y)^3-(x-y)^3-6y(x^2-y^2)$
Option 1: $8y^3$
Option 2: $x^3$
Option 3: $8x^2$
Option 4: $y^3$
Question : If $\frac{x}{4 y}=\frac{3}{4}$ then, the value of $\frac{2 x+3 y}{x–2 y}$ is:
Option 1: 7
Option 3: 6
Option 4: 8
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