prove that A+B(A+C)+AC=A+BC

asked by guest
on Dec 08, 2023 at 1:51 am



You asked:

Prove or disprove that the equation $A + B \left(A + C\right) + A C = A + B C$ is an identity.

MathBot Answer:

The left-hand side of the equation evaluates to:

\[\begin{align*}& A + B \left(A + C\right) + A C\\=& A + A B + B C + A C\\=& A B + A C + B C + A\\\end{align*}\]

The right-hand side of the equation evaluates to:

\[\begin{align*}& A + B C\\=& B C + A\\\end{align*}\]

Since $A B + A C + B C + A \ne B C + A$, the equation $A + B \left(A + C\right) + A C = A + B C$ is not an identity.

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