Worked Example 1
Simplify 4a²b × 3ab³.
Deal with the numbers first4 × 3 = 12
Now each letter in turna² × a¹ = a³, and b¹ × b³ = b⁴
Put it together12a³b⁴
Check by counting lettersThree a's and four b's altogether. This always settles a power rule.
Worked Example 2
Expand and simplify 3(2x + 5) − 2(x − 4).
First bracket3(2x + 5) = 6x + 15
Second bracket, with the minus−2(x − 4) = −2x + 8
Collect like terms4x + 23
Check with x = 1Original: 3(7) − 2(−3) = 21 + 6 = 27. Answer: 4 + 23 = 27.
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