Substitution

Substitution means replacing letters in an expression with the values you are given. Use brackets when a value is being multiplied or when the value is negative, then work out the expression using the correct order of operations.

Common mistake: When substituting a negative number, use brackets. If \(p = -4\), then \(p^2\) means \((-4)^2 = 16\), not writing \(-4^2\) without brackets.

Worked example:
If \(x = 4\) and \(y = 2\), work out \(3x + 2y\).
  1. Substitute x = 4 and y = 2.
    \[3(4) + 2(2)\]
    \[12 + 4 = 16\]
Answer:
\[3x + 2y = 16\]
Worked example:
If \(a = -3\) and \(b = 5\), work out \(a^2 + 2b\).
  1. Substitute a = -3 and b = 5. Use brackets for the negative number.
    \[(-3)^2 + 2(5)\]
    \[9 + 10 = 19\]
Answer:
\[a^2 + 2b = 19\]
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