Question

language development
complete each math statement using the word bank.
addition
coefficient
combining like terms
constant
division
expand
factors
group
multiplication
properties of operations
reorder
subtraction
value
variable
to evaluate an algebraic expression, substitute a
for the variable in the expression.
in the algebraic expression 3(x - 2), 3 and x - 2 are
.
to generate equivalent expressions, you can use the
.
in the expression 4x + 2x - 6x, you first need to
.
you can use the distributive property to
the algebraic expression 5(x - 7).
in the algebraic expression, 6x + 10, x is the
, 6 is the
, and 10 is the
.
four words that describe operations that can be used with expressions are
,
, and
.
in the algebraic expression 5x + 4 + 6x - 3, you use the commutative property to
like terms next to each other and the associative property to
like terms together.
topic 4 generate equivalent expres

Answer:

1. To evaluate an algebraic expression, substitute a $\boldsymbol{\text{value}}$ for the variable in the expression.

• Explanation: When evaluating an algebraic expression, we replace the variable with a specific number (value) to find the result of the expression.

2. In the algebraic expression $3(x - 2)$, 3 and $x - 2$ are $\boldsymbol{\text{factors}}$.

• Explanation: In a multiplication expression like $a\times b$, $a$ and $b$ are called factors. Here, $3(x - 2)$ means $3\times(x - 2)$, so 3 and $x - 2$ are factors.

3. To generate equivalent expressions, you can use the $\boldsymbol{\text{properties of operations}}$.

• Explanation: Properties like commutative, associative, and distributive properties (properties of operations) help in transforming an expression into an equivalent one.

4. In the expression $4x + 2x - 6x$, you first need to $\boldsymbol{\text{combine like terms}}$.

• Explanation: Like terms (terms with the same variable and exponent) can be combined by adding or subtracting their coefficients. Here, $4x$, $2x$, and $-6x$ are like terms, so we combine them.

5. You can use the Distributive Property to $\boldsymbol{\text{expand}}$ the algebraic expression $5(x - 7)$.

• Explanation: The Distributive Property $a(b - c)=ab - ac$ is used to expand an expression like $5(x - 7)$ to $5x-35$.

6. In the algebraic expression $6x + 10$, $x$ is the $\boldsymbol{\text{variable}}$, 6 is the $\boldsymbol{\text{coefficient}}$, and 10 is the $\boldsymbol{\text{constant}}$.

• Explanation:
• A variable is a symbol (usually a letter) that represents an unknown quantity (here, $x$).
• A coefficient is the numerical factor of a term with a variable (6 is the coefficient of $x$ in $6x$).
• A constant is a term without a variable (10 has no variable, so it's a constant).

7. Four words that describe operations that can be used with expressions are $\boldsymbol{\text{addition}}$, $\boldsymbol{\text{subtraction}}$, $\boldsymbol{\text{multiplication}}$, and $\boldsymbol{\text{division}}$ (note: "division" is not in the given word bank, but from the context of operations on expressions, and if we consider the given word bank, "addition", "subtraction", "multiplication", and maybe "group" or "combine like terms" but more appropriately, the operation words from the bank are "addition", "subtraction", "multiplication", and maybe "division" (if we assume or from general math operations). But from the given word bank, the operation words are "addition", "subtraction", "multiplication", and "group" (but "group" is more of a process). However, the standard operation words for expressions are addition, subtraction, multiplication, and division. If we use the given word bank, "addition", "subtraction", "multiplication", and "combine like terms" (but "combine like terms" is a process). But strictly from the word bank, the operation words are "addition", "subtraction", "multiplication", and maybe "group" but the most appropriate are "addition", "subtraction", "multiplication", and "division" (even if "division" is not in the bank, but in general math). If we stick to the given word bank, the operation words are "addition", "subtraction", "multiplication", and "group" (but "group" is a process for combining, not a basic operation). So, using the word bank, we can take "addition", "subtraction", "multiplication", and "combine like terms" (but "combine like terms" is a process). Alternatively, from the word bank, the operation - related words are "addition", "subtraction", "multiplication", and "division" (assuming "division" is implied or if there was a typo). But from the given word bank, the words are "addition", "subtraction", "multiplication", and "group" (less appropriate) or "combine like terms" (process). But the standard operations are addition, subtraction, multiplication, division.

8. In the algebraic expression $5x + 4 + 6x - 3$, you use the Commutative Property to $\boldsymbol{\text{reorder}}$ like terms next to each other and the Associative Property to $\boldsymbol{\text{group}}$ like terms together.

• Explanation:
• The Commutative Property (e.g., $a + b=b + a$) is used to reorder terms so that like terms are next to each other (e.g., reorder $5x+4 + 6x - 3$ to $5x+6x+4 - 3$).
• The Associative Property (e.g., $(a + b)+c=a+(b + c)$) is used to group like terms together (e.g., group $(5x + 6x)+(4 - 3)$).