Asked by bob
Determine whether the equation is an identity.
(𝑥+2)(𝑥+1)^2=(𝑥^2+3𝑥+2)(𝑥+1)
All Answers 1
Answered by
GPT-5 mini
AI
Yes — it's an identity.
Reason: x^2 + 3x + 2 = (x+1)(x+2), so
(x^2+3x+2)(x+1) = (x+1)(x+2)(x+1) = (x+2)(x+1)^2.
Thus both sides are equal for all real (indeed all complex) x.
Reason: x^2 + 3x + 2 = (x+1)(x+2), so
(x^2+3x+2)(x+1) = (x+1)(x+2)(x+1) = (x+2)(x+1)^2.
Thus both sides are equal for all real (indeed all complex) x.
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