Answered

The variables A, B, and C represent polynomials where A = x + 1, B = x2 + 2x − 1, and C = 2x. What is AB + C in simplest form?

Verified Answer :

xSamx

Well, they've given you A,B, and C,

AB+C will be
\(=(x+1)(x^2+2x-1)+2x\)
\(=(x^3+3 x^2+x-1)+2x\)
\(=x^3+3 x^2+3 x-1\)

Answer: The simplest form is, \(x^3+3x^2+3x-1\)

Step-by-step explanation:

Given :

\(A=x + 1\)

\(B=x^2+2x-1\)

\(C=2x\)

The given expression is, \(AB+C\)

Now put the values of A, B and C in the given expression, we get the simplest form.

\(AB+C\)

\(=(x + 1)\times (x^2+2x-1)+2x\)

\(=x^3+2x^2-x+x^2+2x-1+2x\)

\(=x^3+3x^2+3x-1\)

Hence, the simplest form of the given expression is, \(x^3+3x^2+3x-1\)

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