Maya was asked whether the following equation is an identity:(2x+3)(x+1)=2(x+1)2+(x+1)She performed the following steps:(2x+3)(x+1)↪ Step 1=2x2+2x+3x+3↪ Step 2=2x2+4x+2+x+1↪ Step 3=2(x2+2x+1)+(x+1)↪ Step 4=2(x+1)2+(x+1)For this reason, Maya stated that the equation is a true identity.Is Maya correct? If not, in which step did she make a mistake?Choose 1 answer:(A) Maya is correct.(B) Maya is incorrect. She made a mistake in step 1.(C) Maya is incorrect. She made a mistake in step 2 .(D) Maya is incorrect. She made a mistake in step 4.
Q. Maya was asked whether the following equation is an identity:(2x+3)(x+1)=2(x+1)2+(x+1)She performed the following steps:(2x+3)(x+1)↪ Step 1=2x2+2x+3x+3↪ Step 2=2x2+4x+2+x+1↪ Step 3=2(x2+2x+1)+(x+1)↪ Step 4=2(x+1)2+(x+1)For this reason, Maya stated that the equation is a true identity.Is Maya correct? If not, in which step did she make a mistake?Choose 1 answer:(A) Maya is correct.(B) Maya is incorrect. She made a mistake in step 1.(C) Maya is incorrect. She made a mistake in step 2 .(D) Maya is incorrect. She made a mistake in step 4.
Combine Terms: Combine like terms.2x2+2x+3x+3=2x2+5x+3
Rewrite Equation: Rewrite the right-hand side of the equation.2(x+1)2+(x+1)=2(x2+2x+1)+x+1
Expand Right Side: Expand the right-hand side.2(x2+2x+1)+x+1=2x2+4x+2+x+1
Combine Like Terms: Combine like terms on the right-hand side.2x2+4x+2+x+1=2x2+5x+3
Compare Sides: Compare the left-hand side and the right-hand side. Since both sides are equal, Maya's equation is an identity.
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