Algebraic Expressions and Polynomials Review

A set of vocabulary flashcards covering algebraic operations including polynomial addition, monomial multiplication/division, expression evaluation, and radical simplification.

Polynomial Addition: $3x^2 + (-x^2 + 4xy) + (x^2 + 2xy - 3)$

$$3x^2 + 6xy - 9$$

Subtraction of Monomials: $8x^4 - 2x^4$

$$6x^4$$

Product of Monomials: $(8x^4)(-2x^4)$

$$-16x^8$$

Division of Monomials: $\frac{8x^4}{2x^4}$

$$4$$

Distributive Simplification: $2x(x-5) - 2x$

$$2x^2 - 12x$$

Distributive Simplification: $3x(x + 2) - 5(x^2 + 3x)$

$$-2x^2 - 9x$$

Polynomial Division: $\frac{x^4 - 6x^2 - 1}{x^2}$

$$x^2 - 6 - \frac{1}{x^2}$$

Evaluating expressions: $\frac{6ac}{5b}$ where $a=3, b=0, c=-1$

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Zero Exponent Property: $(a + c)^0$

$$1$$

Evaluating expressions: $a^2 c^3$ where $a=3, c=-1$

$$-9$$

Radical Simplification: $\sqrt{9x^2 + 16x^2}$

$$5x$$

Cube Root Simplification: $\sqrt[3]{-27a^3 b^6}$

$$-3ab^2$$