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: $(x+3)(x–3)=x^{2}–9$

Question

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: $(x+3)(x–3)=x^{2}–9$

Team Careers360 · Accepted Answer

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 : An example of an equality relation of two expressions in x. Which is not an identity, is:Option 1: (x+3)2=x2+6x+9Option 2: (x+2y)3=x3+8y3+6xy(x+2y)Option 3: (x+2)2=x2+2x+4Option 4: (x+3)(x–3)=x2–9

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Question : An example of an equality relation of two expressions in $x$ . Which is not an identity, is:
Option 1: $(x + 3)^{2} = x^{2} + 6 x + 9$
Option 2: $(x + 2 y)^{3} = x^{3} + 8 y^{3} + 6 x y (x + 2 y)$
Option 3: $(x + 2)^{2} = x^{2} + 2 x + 4$
Option 4: $(x + 3) (x - 3) = x^{2} - 9$