Algebra – Four Skills – Level 1
This week we have been looking at four different skills applicable to algebra.
Please remember that perfect presentation is essential as we are now dealing with far more
than 15 characters!
Note, all four of these skills are covered in the Beacon maths videos, as part of the algebra
playlist, found at:
http://www.youtube.com/watch?v=6E0D-Icy-QY&list=PL97CDFF468267F9FC
Skill One – Collecting Like Terms or “Simplifying”
When asked to collect like terms, you need to gather together the terms which have identical
letter combinations.
Eg. 7a2 + 13a + 5b – 2a + 6a2 = 13a2 +10a + 5b
Please collect like terms (or simplify) the following expressions. You must write out the
question and the answer.
1. 8a + 4b – 2a + 7b + 8b
2. 9x – 2y – 11x + 8y
3. 16t + 7s + 2t – 3s + 5
4. 9a2 + 2b + 2a2 – 6b – a2
5. 4a2b – ab + 3a2b - 8ab
Skill Two – Multiplying Algebraic Terms
When multiplying algebraic terms, we multiply the coefficients and we add the indices when
the bases are the same.
Eg. 8a3b7c2 x 10a5b2c5 = 80a8b9c7
Please multiply the following. You must write out the question and the answer.
1. 8ab x 9ab2
2. 3a2b3 x 10a6bc
3. 11ab2 x a2b
4. ab2c x 3abc
5. 2ab x 3ab x 6ab
Skill Three – Multiplying Out Brackets
When multiplying out brackets, the terms inside the bracket are each multiplied by the term
outside the brackets. You also need to keep an eye on the sign inside the brackets.
Eg. 9a(4a2 - 7b) = 36a3 – 63ab
Please multiply out the brackets in the following expressions. You must write out the question
and the answer.
1. 9(a – 2b)
2. 10a(3a – 2b2)
3. 8t(2t – 7)
4. 4r2(11r + 3t)
5. t(t – 1)
Skill Four – Factorising
Factorising involves putting brackets into an expression. You need to find the common factors
of the coefficients and also any letters that the terms have in common.
Eg. 10a2b – 5bc = 5b(2a2 – c)
Please try to factorise “fully” the following expressions. You must write out the question and
the answer.
1. 10a + 8b
2. 11t2 – 3t
3. 18ab – 6a
4. 9b2 – 3ab
5. 20t – 20t3