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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 - Multiple Terms

If $$(x+5)(3x + 8) = Ax^2 + Bx + C$$, what is the sum of $$A$$, $$B$$, and $$C$$?

What is the coefficient of $$y$$ in the expansion of the expression $(4x-y+4)(x+2y-1) ?$

Simplify $\left( 9xy - 6y^2 + 15y \right) \div 3y.$

If $$a=-3$$ and $$b=2$$, evaluate $\left(a^2 - 3ab \right) \times \frac{1}{3a} + \left(ab -\frac{b^2}{2} \right) \div 2b.$

Consider the expansion of $$(8x+y) (14 y + x)$$. After combining like terms, how many terms are there in the expression?

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