Expressions - GED Math

1. Evaluate $2x^2 - 3x$ when $x = -2$.

   $14$. $2(-2)^2 - 3(-2) = 2(4) + 6 = 14$. Square the negative before multiplying.

2. Use $C = \frac{5}{9}(F - 32)$ to find $C$ when $F = 212$.

   $100$. $212 - 32 = 180$, and $\frac{5}{9} \times 180 = 100$.

3. Simplify $3x + 5 - x + 2$.

   $2x + 7$. Combine the $x$ terms ($3x - x$) and the constants ($5 + 2$).

4. What does the distributive property state?

   $a(b + c) = ab + ac$. Multiply the outside factor by every term inside the parentheses.

5. Factor out the greatest common factor: $6x^2 + 9x$.

   $3x(2x + 3)$. Both terms share the factor $3x$.

6. What are like terms?

   Terms with the same variable raised to the same power, such as $3x^2$ and $-x^2$. Combine them by adding their coefficients.

7. Write an expression for "7 less than twice a number $n$."

   $2n - 7$. "Less than" reverses the order: start with $2n$ and subtract $7$.

8. Multiply $(x + 3)(x - 5)$.

   $x^2 - 2x - 15$. Multiply each term by each term: $x^2 - 5x + 3x - 15$.

9. Expand $-3(2x - 4)$.

   $-6x + 12$. Distribute $-3$ to both terms: $-3 \cdot 2x = -6x$ and $-3 \cdot (-4) = 12$.

10. Write an expression for "the quotient of a number $n$ and 4, increased by 3."

    $\frac{n}{4} + 3$. "Quotient" means divide, and "increased by" means add.

11. Simplify $\frac{12x^5}{4x^2}$.

    $3x^3$. Divide the coefficients ($12 \div 4$) and subtract the exponents ($5 - 2$).

12. What is the coefficient in the term $5x$?

    $5$. A coefficient is the number that multiplies the variable.

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