UK Secondary (7-11)
Multiply algebraic terms with negatives
Lesson

Remember that when we write algebraic terms such as $2y$2y, this means $2$2 groups of $y$y and there is an unwritten multiplication sign between the $2$2 and the $y$y (otherwise we would write it as $2\times y$2×y). So when we are multiplying with numbers and algebraic terms, we can multiply our numbers as normal and then multiply the algebraic terms.

#### Examples

##### Question 1

Question: Simplify the expression $4\times r\times s$4×r×s

Think: that we don't normally write the multiplication sign between letters and numbers

Do: $4rs$4rs (you could also write this as $4sr$4sr)

##### Question 2

Question: What term should be written in the space to make this statement true? $8t$8t$\times$×$\text{something }$something $=$=$56t$56t

Think: $8$8$\times$×7$=$=$56$56. The $t$t does not have to change.

Do: $7$7 should be written in the space.

#### More examples

##### Question 3

Simplify the expression $8m\times2m$8m×2m.

##### Question 4

Simplify the expression $\left(-2pq\right)\times6q\times\left(-2n\right)$(2pq)×6q×(2n).

##### Question 5

Simplify the expression $\frac{1}{9}\times45uvw\times8w$19×45uvw×8w.