Algebraic Expressions: Expand, Simplify and Substitute

Lesson focus

Algebra is a compact way to describe a changing quantity. In this lesson, you will use brackets, match like terms, and replace letters with values accurately.

Read the worked examples slowly, then use the practice and quiz to check your understanding.

Like terms and brackets

Only terms with the same variable part can be collected. For example, $3x$ and $-7x$ are like terms, but $3x$ and $3x^2$ are not.

Worked example

Simplify $4(2x-3)-5x+7$.

Step 1

Expand the bracket: $4(2x-3)=8x-12$.

Step 2

Group the like terms: $8x$ and $-5x$ are variable terms; $-12$ and $+7$ are constants.

Step 3

$4(2x-3)-5x+7=$8x-5x$+$-12+7$=3x-5$.

Substitution

Use brackets when you substitute a negative number.

Worked example

If $x=-2$ and $y=3$, evaluate $2x^2-3xy+y$.

Step 1

Replace each letter with its value, keeping the negative value in brackets: $2(-2)^2-3(-2)(3)+3$.

Step 2

$2(-2)^2-3(-2)(3)+3=8+18+3=29$.

Before you leave

When simplifying, collect only matching terms. When substituting a negative number, use brackets before calculating.