Algebraic Expressions: Expand, Simplify and Substitute
Turn algebra language into accurate expressions and avoid common bracket mistakes.
Lesson focus
Algebra is a compact way to describe a changing quantity. Use brackets carefully, collect like terms, and replace letters with values accurately.
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
$4(2x-3)-5x+7=8x-5x-12+7$
$8x-5x-12+7=3x-5$
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
$2(-2)^2-3(-2)(3)+3=8+18+3$
$8+18+3=29$
Practice Problems
Attempt each question before opening its answer.
Practice 1
Simplify $5(2y-1)-3(y+4)$
Show answer
Step 1
Expand both brackets: $10y-5-3y-12$
Step 2
Collect like terms: $10y-5-3y-12=7y-17$
Practice 2
Explain why $3(x+4)=3x+4$ is wrong.
Show answer
The 3 must multiply both terms: $3(x+4)=3x+12$
Interactive Quiz
Check one key idea.