GRE Quantitative Flashcards: Algebraic Expressions Simplification

What this deck covers

This deck focuses on Algebraic Expressions Simplification, giving you a quick way to review the definitions, rules, and examples that matter most for GRE Quantitative.

How to use these flashcards

Work through these flashcards in short sessions. Try to answer each prompt before flipping the card, then revisit any cards you miss until the explanation feels automatic.

Flashcard 1: What is the simplified form of $(x^3)^2$?

Answer: $x^6$. Raise a power to a power by multiplying exponents: $3 cdot 2 = 6$.

Flashcard 2: What is the simplified form of rac{3x}{4}-rac{x}{8}?

Answer: rac{5x}{8}. Subtract fractions with common denominator 8: rac{6x}{8} - rac{x}{8} = rac{5x}{8}.

Flashcard 3: What is the simplified form of rac{x^2-4}{x^2+4x+4} for $x\ne -2$?

Answer: rac{x-2}{x+2}. Factor numerator as $(x-2)(x+2)$ and denominator as $(x+2)^2$, then cancel one $(x+2)$.

Flashcard 4: What property justifies rewriting $ab+ac$ as $a(b+c)$?

Answer: Factoring using the distributive property. Factoring reverses the distributive property by extracting the common factor $a$ from $ab + ac$ to form $a(b + c)$.

Flashcard 5: What is the simplified form of $x^2-10x+25$?

Answer: $(x-5)^2$. Factor as perfect square trinomial: coefficients fit $(x-5)^2 = x^2 - 10x + 25$.

Flashcard 6: What is the simplified form of $3x+5x$?

Answer: $8x$. Combine like terms by adding the coefficients of $x$, resulting in $3 + 5 = 8$.

Flashcard 7: What is the simplified form of $(x-5)(x+5)$?

Answer: $x^2-25$. Apply difference of squares formula: $x^2 - 5^2$.

Flashcard 8: What is the simplified form of rac{2}{3}x+rac{1}{6}x?

Answer: rac{5}{6}x. Add fractions with common denominator 6: rac{4}{6}x + rac{1}{6}x = rac{5}{6}x.

Flashcard 9: What is the simplified form of $x^0$ for $x\ne 0$?

Answer: $1$. Any non-zero number raised to the power of 0 equals 1 by definition.

Flashcard 10: What is the simplified form of $x^{-3}$ using only positive exponents?

Answer: rac{1}{x^3}. A negative exponent indicates a reciprocal with the exponent made positive.

Flashcard 11: What is the simplified form of $7a-2a+9a$?

Answer: $14a$. Combine like terms by computing the net coefficient: $7 - 2 + 9 = 14$.

Flashcard 12: What is the simplified form of $-(x-6)+2(x+1)$?

Answer: $x+8$. Distribute the negative and the 2, then combine like terms: $-x + 6 + 2x + 2 = x + 8$.

Flashcard 13: What is the simplified form of rac{x^2-9}{x-3} for $x\ne 3$?

Answer: $x+3$. Factor numerator as $(x-3)(x+3)$ and cancel common factor $(x-3)$ with denominator.

Flashcard 14: What is the simplified form of rac{6a^3b^2}{2ab^5} using only positive exponents?

Answer: rac{3a^2}{b^3}. Convert negative exponent to positive by moving $b^{-3}$ to the denominator as $b^3$.

Flashcard 15: What property justifies rewriting $a(b+c)$ as $ab+ac$?

Answer: Distributive property. The distributive property states that multiplication distributes over addition, allowing $a(b+c)$ to expand to $ab + ac$.

Flashcard 16: What is the simplified form of $(x^{-2})(x^5)$ for $x\ne 0$?

Answer: $x^3$. Multiply powers with the same base by adding exponents: $-2 + 5 = 3$.

Flashcard 17: What is the simplified form of rac{x^2+5x}{x} for $x\ne 0$?

Answer: $x+5$. Factor $x$ from numerator and cancel with denominator: rac{x(x+5)}{x} = x+5.

Flashcard 18: What is the simplified form of $(x+3)^2$?

Answer: $x^2+6x+9$. Expand using FOIL or square binomial formula: $x^2 + 2cdot xcdot 3 + 3^2$.

Flashcard 19: What is the simplified form of rac{1}{x^{-2}} for $x\ne 0$?

Answer: $x^2$. The reciprocal of a negative exponent simplifies to the base with a positive exponent: $x^{-(-2)} = x^2$.

Flashcard 20: What is the simplified form of $4(x-3)+2x$?

Answer: $6x-12$. Distribute the 4 and combine like terms: $4x - 12 + 2x = 6x - 12$.

Flashcard 21: What is the simplified form of $(2x^2y)^3$?

Answer: $8x^6y^3$. Distribute the exponent to each factor: $2^3=8$, $(x^2)^3=x^6$, $y^3=y^3$.

Flashcard 22: What is the simplified form of rac{x^5}{x^2} for $x\ne 0$?

Answer: $x^3$. Divide powers with the same base by subtracting exponents: $5 - 2 = 3$.