SAT Math Flashcards: Equivalent Expressions

What this deck covers

This deck focuses on Equivalent Expressions, giving you a quick way to review the definitions, rules, and examples that matter most for SAT Math.

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 $3x + 4x$?

Answer: 7x. Combine like terms by adding coefficients.

Flashcard 2: Simplify the expression $\frac{3x}{2} + \frac{x}{2}$.

Answer: $2x$. Add fractions with same denominator: $\frac{3x + x}{2} = \frac{4x}{2} = 2x$.

Flashcard 3: What is the expanded form of $(3x - 2)^2$?

Answer: $9x^2 - 12x + 4$. Expand using $(a - b)^2 = a^2 - 2ab + b^2$.

Flashcard 4: Identify the equivalent expression for $x^2 + 2xy + y^2$.

Answer: $(x + y)^2$. Perfect square trinomial pattern: $a^2 + 2ab + b^2 = (a + b)^2$.

Flashcard 5: Simplify: $-4(a - 2) + 3a$.

Answer: $-a + 8$. Distribute -4, then combine like terms.

Flashcard 6: Simplify: $2(3a + 4) - 5a$.

Answer: $a + 8$. Distribute 2, then combine like terms.

Flashcard 7: What is the simplified form of $2x + 3x$?

Answer: $5x$. Combine like terms by adding coefficients.

Flashcard 8: What is the simplified form of $3x + 4x$?

Answer: 7x. Combine like terms by adding coefficients.

Flashcard 9: Which expression is equivalent to $-3(x - 2) + 4x$?

Answer: $x + 6$. Distribute -3, then combine like terms.

Flashcard 10: Simplify the expression: $2(x + 5) - 3x$.

Answer: $-x + 10$. Distribute 2, then combine like terms.

Flashcard 11: What is the simplified form of $6 - 2(3 - x)$?

Answer: $2x$. Distribute -2, then combine like terms.

Flashcard 12: State the distributive property formula.

Answer: $a(b + c) = ab + ac$. Multiplying distributes over addition inside parentheses.

Flashcard 13: Identify the like terms in $7x^2 + 3x - 2x^2 + 4$.

Answer: $7x^2$ and $-2x^2$. Like terms have the same variable and exponent.

Flashcard 14: Simplify: $5y - 3 + 2y + 7$.

Answer: $7y + 4$. Group like terms and combine coefficients.

Flashcard 15: What is the commutative property of multiplication?

Answer: $ab = ba$. Order doesn't matter in multiplication.

Flashcard 16: Simplify the expression: $2(3x - 4) + 5x$.

Answer: $11x - 8$. Distribute 2, then combine like terms.

Flashcard 17: Simplify: $3(x + 2) - 4(x - 1)$.

Answer: $-x + 10$. Distribute both terms, then combine like terms.

Flashcard 18: Which expression is equivalent to $8 - (2x - 3)$?

Answer: $11 - 2x$. Distribute negative sign, then combine like terms.

Flashcard 19: Which expression is equivalent to $2(x + 4) + 3$?

Answer: $2x + 11$. Distribute 2, then add 3.

Flashcard 20: What is the associative property of addition?

Answer: $(a + b) + c = a + (b + c)$. Grouping doesn't change the sum.

Flashcard 21: Simplify: $6 - (3x + 2) + 4x$.

Answer: $x + 4$. Distribute negative, then combine like terms.

Flashcard 22: Simplify the expression: $4(y - 3) + 2y$.

Answer: $6y - 12$. Distribute 4, then combine like terms.

Flashcard 23: What is the identity property of multiplication?

Answer: $a \times 1 = a$. Multiplying by 1 doesn't change the value.

Flashcard 24: Which expression is equivalent to $-3(x - 2) + 4x$?

Answer: $x + 6$. Distribute -3, then combine like terms.

Flashcard 25: What is the simplified form of $3(x + 2) - x$?

Answer: $2x + 6$. Distribute 3, then combine like terms.

Flashcard 26: What is the inverse property of multiplication?

Answer: $a \times \frac{1}{a} = 1$ for $a \neq 0$. Multiplying by reciprocal gives 1.

Flashcard 27: Which expression is equivalent to $x(x - 3) + x$?

Answer: $x^2 - 2x$. Distribute $x$, then combine like terms.

Flashcard 28: What is the identity property of addition?

Answer: $a + 0 = a$. Adding zero doesn't change the value.

Flashcard 29: Which expression is the simplest form of $5x - 3x + 2$?

Answer: $2x + 2$. Combine like terms by adding coefficients.

Flashcard 30: What is the simplified form of $2x + 3(x - 1)$?

Answer: $5x - 3$. Distribute 3, then combine like terms.