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Mustafa was asked whether the following equation is an identity:

x(9x+3)+3(x+3)=9(x+1)^(2)
He performed the following steps:

x(9x+3)+3(x+3)

rarr"" Step "1"=9x^(2)+6x+9

longrightarrow^(" Step 2 ")=(3x+3)^(2)

harr^(" Step "3)=(3(x+1))^(2)

longrightarrow^(" Step "4)=9(x+1)^(2)
For this reason, Mustafa stated that the equation is a true identity.
Is Mustafa correct? If not, in which step did he make a mistake?
Choose 1 answer:
(A) Mustafa is correct.
(B) Mustafa is incorrect. He made a mistake in step 1.
(C) Mustafa is incorrect. He made a mistake in step 2.
(D) Mustafa is incorrect. He made a mistake in step 4.

Mustafa was asked whether the following equation is an identity:\newlinex(9x+3)+3(x+3)=9(x+1)2 x(9 x+3)+3(x+3)=9(x+1)^{2} \newlineHe performed the following steps:\newlinex(9x+3)+3(x+3) x(9 x+3)+3(x+3) \newline Step 1=9x2+6x+9 \stackrel{\text { Step } 1}{\hookrightarrow}=9 x^{2}+6 x+9 \newline Step 2=(3x+3)2 \stackrel{\text { Step } 2}{\hookrightarrow}=(3 x+3)^{2} \newline Step 3=(3(x+1))2 \stackrel{\text { Step } 3}{\hookrightarrow}=(3(x+1))^{2} \newline Step 4=9(x+1)2 \stackrel{\text { Step } 4}{\hookrightarrow}=9(x+1)^{2} \newlineFor this reason, Mustafa stated that the equation is a true identity.\newlineIs Mustafa correct? If not, in which step did he make a mistake?\newlineChoose 11 answer:\newline(A) Mustafa is correct.\newline(B) Mustafa is incorrect. He made a mistake in step 11.\newline(C) Mustafa is incorrect. He made a mistake in step 22.\newline(D) Mustafa is incorrect. He made a mistake in step 44.

Full solution

Q. Mustafa was asked whether the following equation is an identity:\newlinex(9x+3)+3(x+3)=9(x+1)2 x(9 x+3)+3(x+3)=9(x+1)^{2} \newlineHe performed the following steps:\newlinex(9x+3)+3(x+3) x(9 x+3)+3(x+3) \newline Step 1=9x2+6x+9 \stackrel{\text { Step } 1}{\hookrightarrow}=9 x^{2}+6 x+9 \newline Step 2=(3x+3)2 \stackrel{\text { Step } 2}{\hookrightarrow}=(3 x+3)^{2} \newline Step 3=(3(x+1))2 \stackrel{\text { Step } 3}{\hookrightarrow}=(3(x+1))^{2} \newline Step 4=9(x+1)2 \stackrel{\text { Step } 4}{\hookrightarrow}=9(x+1)^{2} \newlineFor this reason, Mustafa stated that the equation is a true identity.\newlineIs Mustafa correct? If not, in which step did he make a mistake?\newlineChoose 11 answer:\newline(A) Mustafa is correct.\newline(B) Mustafa is incorrect. He made a mistake in step 11.\newline(C) Mustafa is incorrect. He made a mistake in step 22.\newline(D) Mustafa is incorrect. He made a mistake in step 44.
  1. Expand and Simplify: Check if the right side of the equation simplifies to the same expression.\newline9(x+1)2=9(x2+2x+1)9(x+1)^{2} = 9(x^2 + 2x + 1)\newlineExpand the squared term.\newline=9x2+18x+9= 9x^2 + 18x + 9
  2. Compare Left and Right: Compare the left side from Step 11 with the right side from Step 22.\newlineLeft side: 9x2+6x+99x^2 + 6x + 9\newlineRight side: 9x2+18x+99x^2 + 18x + 9\newlineThe two expressions are not equal because the coefficients of xx are different.

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