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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...

# Distributive Property Misconceptions

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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