MIHLE MBANGATA 218091915
MATHS 2 - ASSIGNMENT 1: ALGEBRAIC FRACTIONS
1. Simplify each of the following!
27𝑥 6 𝑦 3
1.1.
18𝑥 2 𝑦 5
9(3𝑥 4 )
=
9(2𝑦 2 )
3𝑥 4
=
2𝑦 2
𝑥 2 −16
1.2. (4−𝑥)2
(𝑥 − 4)(𝑥 + 4)
=
(4 − 𝑥)2
(𝑥−4)(𝑥+4)
= [a negative raised to an even power equal a positive]
−(𝑥−4)2
𝑥+4
=
𝑥−4
4𝑎3 −32
1.3.
𝑎2 −4𝑎+4
4(𝑎3 − 8)
=
(𝑎 − 2)(𝑎 − 2)
4(𝑎 − 2)(𝑎2 + 2𝑎 + 4)
=
(𝑎 − 2)(𝑎 − 2)
4𝑎2 + 8𝑎 + 16
=
𝑎−2
MATHS 2 - ASSIGNMENT 1: ALGEBRAIC FRACTIONS
1. Simplify each of the following!
27𝑥 6 𝑦 3
1.1.
18𝑥 2 𝑦 5
9(3𝑥 4 )
=
9(2𝑦 2 )
3𝑥 4
=
2𝑦 2
𝑥 2 −16
1.2. (4−𝑥)2
(𝑥 − 4)(𝑥 + 4)
=
(4 − 𝑥)2
(𝑥−4)(𝑥+4)
= [a negative raised to an even power equal a positive]
−(𝑥−4)2
𝑥+4
=
𝑥−4
4𝑎3 −32
1.3.
𝑎2 −4𝑎+4
4(𝑎3 − 8)
=
(𝑎 − 2)(𝑎 − 2)
4(𝑎 − 2)(𝑎2 + 2𝑎 + 4)
=
(𝑎 − 2)(𝑎 − 2)
4𝑎2 + 8𝑎 + 16
=
𝑎−2
