Alaina was asked whether the following equation is an identity:(2x+1)2−(x+1)2=3(x+1)2−1She performed the following steps:(2x+1)2−(x+1)2↪ Step 1=4x2+4x+1−x2+2x+1↪ Step 2=3x2+6x+2↪ Step 3=3x2+6x+3−1↪ Step 4=3(x2+2x+1)−1↪ Step 5=3(x+1)2−1For this reason, Alaina stated that the equation is a true identity.Is Alaina correct? If not, in which step did she make a mistake?Choose 1 answer:(A) Alaina is correct.(B) Alaina is incorrect. She made a mistake in step 1.(C) Alaina is incorrect. She made a mistake in step 3.(D) Alaina is incorrect. She made a mistake in step 5.
Q. Alaina was asked whether the following equation is an identity:(2x+1)2−(x+1)2=3(x+1)2−1She performed the following steps:(2x+1)2−(x+1)2↪ Step 1=4x2+4x+1−x2+2x+1↪ Step 2=3x2+6x+2↪ Step 3=3x2+6x+3−1↪ Step 4=3(x2+2x+1)−1↪ Step 5=3(x+1)2−1For this reason, Alaina stated that the equation is a true identity.Is Alaina correct? If not, in which step did she make a mistake?Choose 1 answer:(A) Alaina is correct.(B) Alaina is incorrect. She made a mistake in step 1.(C) Alaina is incorrect. She made a mistake in step 3.(D) Alaina is incorrect. She made a mistake in step 5.
Expand Expression: Expand (2x+1)2 and (x+1)2.(2x+1)2=4x2+4x+1(x+1)2=x2+2x+1
Subtract Squares: Subtract (x+1)2 from (2x+1)2.4x2+4x+1−(x2+2x+1)=3x2+2x
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