Math Accelerated: Chapter 7 Algebraic Expressions

Vocabulary practice and key algebraic concepts derived from Lesson 1 through Lesson 5 of Math Accelerated Chapter 7.

Distributive Property

The property used to write an expression such as $a(b + c)$ as an equivalent expression $ab + ac$, or $a(b - c)$ as $ab - ac$.

Equivalent Expression

Expressions that have the same value, such as writing $7(y + 11)$ as $7y + 77$.

Evaluate

To find the numerical value of an expression after performing all indicated operations, such as determining that $6(80 + 1)$ equals $486$.

Terms

The parts of an algebraic expression separated by addition or subtraction signs, such as $6y$, $-4$, and $y$ in the expression $6y - 4 + y$.

Like Terms

Terms that contain the same variables, such as $5g$ and $-g$ in the expression $-12h + 5g + 8 - g$.

Coefficients

The numerical part of a term that contains a variable, such as the $-21$ and $3$ in the expression $-21w + 5 + 3w - 1$.

Constants

A term without a variable, such as the $5$ and $-1$ in the expression $-21w + 5 + 3w - 1$.

Simplest Form

An expression that has no like terms and no parentheses, such as $3x + 4$ representing the total cost of items.

Linear Expression

An algebraic expression that can be added or subtracted using models or vertical/horizontal alignment, such as $(5x + 21)$ or $(10x + 13)$.

Total Profit

The resulting expression after adding two separate profit models, such as $(2000x - 10,500) + (1850x - 11,600)$ resulting in $3850x - 22,100$.

Difference in Perimeters

The resulting expression after subtracting the perimeter of one figure from another, calculated as $(5x + 18) - (3x - 2) = 2x + 20$ units.

Monomial

A number, a variable, or a product of a number and one or more variables, such as $20$, $45x$, or $11gh$.

GCF (Greatest Common Factor)

The largest factor shared between a pair of monomials, such as $8m$ being the GCF of $16mn$ and $24m$.

Factoring an Expression

The process of writing a linear expression as a product of its factors, such as factoring $4x + 12$ into $4(x + 3)$.

Cannot be factored

A description for an expression like $32x - 15$ or $25x + 14$ where there is no common factor greater than $1$ for the terms.