MAT1581 Assignment 1 Due 15 May 2026 |Mathematics I (Engineering)|

UNIVERSITY OF SOUTH AFRICA
College of Science, Engineering and Technology


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MAT1581: Mathematics I (Engineering)

Assignment 01 — Semester 1, 2026

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MAT1581
Module Code:
Mathematics I (Engineering)
Module Name:
Assignment 01
Assignment:
Friday, 15 May 2026
Due Date:




Submitted in partial fulfilment of the requirements for MAT1581 — UNISA 2026

,UNISA | MAT1581 Assignment 01 — Due: 15 May 2026



Question 1: Binomial Theorem — Full Expansion


Question 1.1


Expand using the binomial theorem:
(2x − 3y)5


Solution


The binomial theorem for (a − b)5 gives:


(a − b)5 = a5 − 5a4 b + 10a3 b2 − 10a2 b3 + 5ab4 − b5



Let a = 2x and b = 3y. Substituting:


(2x − 3y)5 = (2x)5 − 5(2x)4 (3y) + 10(2x)3 (3y)2 − 10(2x)2 (3y)3 + 5(2x)(3y)4 − (3y)5



Now each term is calculated separately.

Term 1:
(2x)5 = 25 x5 = 32x5


Term 2:
−5(2x)4 (3y) = −5 · 16x4 · 3y = −240x4 y


Term 3:
10(2x)3 (3y)2 = 10 · 8x3 · 9y 2 = 720x3 y 2


Term 4:
−10(2x)2 (3y)3 = −10 · 4x2 · 27y 3 = −1080x2 y 3


Term 5:
5(2x)(3y)4 = 5 · 2x · 81y 4 = 810xy 4


Term 6:
−(3y)5 = −243y 5


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, UNISA | MAT1581 Assignment 01 — Due: 15 May 2026


Combining all terms:


(2x − 3y)5 = 32x5 − 240x4 y + 720x3 y 2 − 1080x2 y 3 + 810xy 4 − 243y 5




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