Question
Real Tutor Solution
Tutor-Verified Answer
Answer
\( 2x^2 + 4x + 2 \)
Solution
Calculate or simplify the expression \( x(x+1)+(x+1)(x+2) \).
Simplify the expression by following steps:
- step0: Solution:
\(x\left(x+1\right)+\left(x+1\right)\left(x+2\right)\)
- step1: Expand the expression:
\(x^{2}+x+\left(x+1\right)\left(x+2\right)\)
- step2: Expand the expression:
\(x^{2}+x+x^{2}+3x+2\)
- step3: Add the terms:
\(2x^{2}+4x+2\)
The simplified form of the expression \( x(x+1)+(x+1)(x+2) \) is \( 2x^2 + 4x + 2 \).
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Simplify this solution Bonus Knowledge
Let's simplify that expression: \( x(x+1)+(x+1)(x+2) \). We can factor out \( (x+1) \) from both terms: 1. The first term becomes \( x(x+1) \). 2. The second term becomes \( (x+1)(x+2) \). So, we have: \[ (x+1)(x) + (x+1)(x+2) = (x+1)(x + (x + 2)) = (x+1)(2x + 2) \] Now we can factor out a 2: \[ = 2(x + 1)(x + 1) = 2(x + 1)^2 \] Thus, the simplified expression is \( 2(x + 1)^2 \). How neat is that? To check your answer, you can expand \( 2(x + 1)^2 \) back out to see if you get the original expression. It’s always satisfying to verify that your simplifications are on point!
