Factor algebraic terms
We've already learnt how to factorise (or add brackets to) equations but only when these equations have common factors that are numbers. Now we are going to look at number sentences that have both numbers and algebraic terms as factors.
Remember that powers indicate that a value is multiplied by itself. For example, $a^3$a3 means $a\times a\times a$a×a×a. For a refresher on algebraic multiplication and division, click here.
Examples
example 1
Factorise: $a^2-3a$a2−3a
Think: There is no common numerical factor. There is a common algebraic factor. The highest algebraic factor is $a$a. So the HCF is $a$a.
Do:
| $a\times a$a×a | $=$= | $a^2$a2 |
| $a\times\left(-3\right)$a×(−3) | $=$= | $-3a$−3a |
| $a^2-3a$a2−3a | $=$= | $a\left(a-3\right)$a(a−3) |
example 2
Factorise: $18w^4-27w^2$18w4−27w2
Think: The highest common numerical factor is $9$9. The highest common algebraic factor is $w^2$w2. So the HCF is $9w^2$9w2.
Do:
| $9w^2\times2w^2$9w2×2w2 | $=$= | $18w^4$18w4 |
| $9w^2\times\left(-3\right)$9w2×(−3) | $=$= | $-27w^2$−27w2 |
| $18w^4-27w^2$18w4−27w2 | $=$= | $9w^2\left(2w^2-3\right)$9w2(2w2−3) |
More examples
Question 1
Factorise: $y^2+4y$y2+4y
Question 2
Fill in the boxes to complete the equality:
$11u-19u^2=u\left(\editable{}-\editable{}\right)$11u−19u2=u(−)
question 3
Factorise: $2u^2-8u$2u2−8u
question 4
Factorise the following expression:
$z^2+4z^5$z2+4z5