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1.08 Identifying and evaluating algebraic expressions

Lesson

Identifying components of algebraic expressions

Recall some of the components of algebraic expressions.  An expression is a representation of a quantity that may contain numbers, variables or operation symbols.  For each of the algebraic expressions below, we can identify each type of component.

Component Algebraic expresison Example
Variables $x^2-x-6$x2x6 $x$x
Terms $x^2-x-6$x2x6 $x^2$x2, $-x$x, and $-6$6
Constant Terms $x^2-x-6$x2x6 $-6$6
Like Terms $x^2-x-6+3x^2$x2x6+3x2 $x^2$x2 and $3x^2$3x2
Coefficients $3x^2-x-6$3x2x6 $3$3 is a coefficient of $x^2$x2$-1$1 is a coefficient of $x$x

 

Practice questions

Question 1

Which of the following best describes an algebraic expression?

  1. A collection of variables, grouping symbols, and operations.

    A

    A collection of numbers and operations.

    B

    A letter of the alphabet used to represent numbers.

    C

    A collection of variables, numbers, grouping symbols, and operations.

    D

QUESTION 2

Choose the best answer for each of the questions below.

  1. What is a variable?

    A symbol that represents a value, which is unknown or arbitrary.

    A

    A term that does not contain numbers.

    B

    A non-numerical symbol.

    C

    A letter of the alphabet.

    D
  2. What is a constant term?

    The numerical factor of a term.

    A

    A term that does not contain numbers.

    B

    A term that does not contain variables.

    C

    The numerical power of a term.

    D

 

Substituting into algebraic expressions

We often want to substitute values for the variables in an algebraic expression. That way we can evaluate the expression to yield a numerical result. Let’s go through an example below.

Worked example

Question 3

Evaluate: Consider the algebraic expression $a^2+2ab-4c^2+\sqrt{a}$a2+2ab4c2+a. Let's evaluate this expression when $a=4$a=4$b=3$b=3 and $c=2$c=2.

Think: Substituting $a=4$a=4$b=3$b=3 and $c=2$c=2, the expression becomes:

$a^2+2ab-4c^2+\sqrt{a}$a2+2ab4c2+a $=$= $\left(4\right)^2+2\times\left(4\right)\times\left(3\right)-4\left(2\right)^2+\sqrt{\left(4\right)}$(4)2+2×(4)×(3)4(2)2+(4)

 

Do: We then need to follow the order of operations to evaluate

$a^2+2ab-4c^2+\sqrt{a}$a2+2ab4c2+a $=$= $\left(4\right)^2+2\times\left(4\right)\times\left(3\right)-4\left(2\right)^2+\sqrt{\left(4\right)}$(4)2+2×(4)×(3)4(2)2+(4)
  $=$= $16+24-16+2$16+2416+2
  $=$= $26$26

 

Reflect: Notice how the order of operations stays the same when we are evaluating expressions.

 

Practice questions

question 4

Evaluate $\left(u+v\right)\left(w-y\right)$(u+v)(wy) when $u=5$u=5, $v=8$v=8, $w=2$w=2 and $y=10$y=10.

QUESTION 5

Find the value of $\frac{x^2}{3}+\frac{y^3}{2}$x23+y32 when $x=-4$x=4 and $y=3$y=3.

question 6

For $x=5$x=5 and $y=4$y=4,

Evaluate: $\sqrt{2x^2+4y+6}$2x2+4y+6 correct to two decimal places.

Outcomes

I.A.SSE.1.a

Interpret parts of an expression, such as terms, factors, and coefficients.

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