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# Properties of Arithmetic

Understanding the properties of arithmetic will allow you to simplify complex expressions and do difficult calculations in a flash. Just don't divide by 0...

Which expression is equivalent to \(3(x^{2}+2x+3)?\)

\[\text{A: }3x^{2} + 6x + 9\] \[\text{B: }3x^{2} + 2x + 3\]

Which expression is equivalent to \(3-(x-2)?\)

\[\text{A: }1-x\] \[\text{B: }5-x\]

Which expression is equivalent to \(\dfrac{3+x}{2+y}?\)

\[\text{A: }\dfrac{3}{2} + \dfrac{x}{y}\] \[\text{B: }\dfrac{3}{2} + \dfrac{x}{2} + \dfrac{3}{y} + \dfrac{x}{y}\]

Which expression is equivalent to \(\sqrt{a+b}?\)

\[\text{A: }\sqrt{a} + \sqrt{b}\] \[\text{B: }\sqrt{a} + 2\sqrt{ab} + \sqrt{b}\]

Which expression is equivalent to \((a \cdot b) + c?\)

\[\text{A: }(a+c)(b+c)\] \[\text{B: }a \cdot (b+c)\]

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