Two rules do all the work: the coefficients multiply and the powers add.
Why the powers add
x² × x³ is x×x multiplied by x×x×x, which is five x's, so x⁵. The powers added because you counted them.
| Multiplication | Coefficients | Letters | Answer |
|---|---|---|---|
| 3x × 5y | 3 × 5 = 15 | x and y stay separate | 15xy |
| 4a × 3a | 4 × 3 = 12 | a¹ × a¹ = a² | 12a² |
| 2x² × 5x³ | 2 × 5 = 10 | x² × x³ = x⁵ | 10x⁵ |
| −3p × 4q | −3 × 4 = −12 | p and q stay separate | −12pq |
In 2x² × 5x³, the 2 and 5 multiply while the powers 2 and 3 add. Writing 10x⁶ means the powers were multiplied.
Multiplying out a bracket
Everything outside multiplies everything inside, without exception. 3(x + 4) is 3x + 12.
A rectangle 3 high and x + 4 long splits into a 3 by x piece and a 3 by 4 piece. Both readings describe the same rectangle.
−2(x − 5) is −2x + 10, not −2x − 10, because −2 × −5 is positive.
Two brackets together
Two brackets of two terms give four products. (x + 2)(x + 3) gives x² + 3x + 2x + 6, which is x² + 5x + 6.
With x = 1, the original is 3 × 4 = 12 and the answer is 1 + 5 + 6 = 12. That check catches a missing product or a lost sign.
The full lesson is waiting for you
Create a free account to unlock activities, practice tests, presentations and videos - and to track your progress and confidence score for every subject.
Simplify 4a²b × 3ab³.
Expand and simplify 3(2x + 5) − 2(x − 4).
1 more worked examples - sign in to see them all.
That's a peek at activity 1 of 4 - sign in for all of them, full length.
Multiplying does NOT need like terms, exactly as multiplying fractions needed no common bottom.
13 more points to remember - sign in to see the rest.
Question 1 of 10
Sign in to watch the video for this topic.