Equivalent Expressions - SAT Math

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

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

2. What is the simplified form of $2x + 3x$?

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

3. What is the simplified form of $3(x + 2) - x$?

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

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

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

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

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

6. What is the simplified form of $3(x + 4) + 2x$?

   $5x + 12$. Distribute 3, then combine like terms.

7. Find the equivalent expression for $2(x - 5) + 3(x + 2)$.

   $5x - 4$. Distribute and combine: $2x - 10 + 3x + 6 = 5x - 4$.

8. Which expression is equivalent to $-3(x - 2) + 4x$?

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

9. What is the simplified form of $2x + 3(x - 1)$?

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

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

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

11. Which expression is equivalent to $x(x - 3) + x$?

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

12. Which expression is equivalent to $8 - (2x - 3)$?

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

13. State the distributive property formula.

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

14. What is the simplified form of $6 - 2(3 - x)$?

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

15. Which expression is equivalent to $4x^2 - 9$?

    $(2x - 3)(2x + 3)$. Difference of squares: $(2x)^2 - 3^2 = (2x - 3)(2x + 3)$.

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

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

17. What is the result of $5(2x - 1) - 3x$?

    $7x - 5$. Distribute 5, then combine like terms.

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

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

19. What is the simplified expression for $7x - (2x + 3)$?

    $5x - 3$. Distribute negative sign, then combine like terms.

20. Identify the like terms in $7x^2 + 3x - 2x^2 + 4$.

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

21. Identify the equivalent expression for $x^2 + 2xy + y^2$.

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

22. Which expression is equivalent to $a^2 - 2ab + b^2$?

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

23. Which expression is equivalent to $5(a + b)$?

    $5a + 5b$. Distribute 5 to both terms inside parentheses.

24. Simplify the expression $2(x + 3) - 4x$.

    $-2x + 6$. Distribute then combine like terms: $2x + 6 - 4x = -2x + 6$.

25. What is the identity property of addition?

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

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

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

27. Which expression is equivalent to $2(x + 4) + 3$?

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

28. What is the associative property of addition?

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

29. Which expression is equivalent to $4(a + 2)$?

    $4a + 8$. Distribute 4 to both terms inside parentheses.

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

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

31. Which expression is the simplest form of $5x - 3x + 2$?

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

32. What is the simplified form of $3x + 4x$?

    7x. Combine like terms by adding coefficients.

33. Simplify: $5y - 3 + 2y + 7$.

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

34. What is the inverse property of multiplication?

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

35. What is the identity property of multiplication?

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

36. What is the expanded form of $(3x - 2)^2$?

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

37. What is the factored form of $x^2 - 4$?

    $(x - 2)(x + 2)$. Difference of squares: $a^2 - b^2 = (a - b)(a + b)$.

38. What is the commutative property of multiplication?

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

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