ABSTRACT
Algebra merely uses letters to represent numbers. If, say, a, b, c and d represent any four numbers then in algebra:
a + a + a + a = 4 a https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429294402/968186b9-ffa4-4f2b-aa54-7fc58a604561/content/eq93.tif"/>
5b means 5 × b
2 a + 3 b + a − 2 b = 2 a + a + 3 b − 2 b = 3 a + b https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429294402/968186b9-ffa4-4f2b-aa54-7fc58a604561/content/eq94.tif"/>
Only similar terms can be combined in algebra.
4 a b c d = 4 × a × b × c × d https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429294402/968186b9-ffa4-4f2b-aa54-7fc58a604561/content/eq95.tif"/>
(a)(c)(d) means a × c × d
Brackets are often used instead of multiplication signs.
a b = b a https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429294402/968186b9-ffa4-4f2b-aa54-7fc58a604561/content/eq96.tif"/>
b 2 = b × b https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429294402/968186b9-ffa4-4f2b-aa54-7fc58a604561/content/eq97.tif"/>
a 3 = a × a × a https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429294402/968186b9-ffa4-4f2b-aa54-7fc58a604561/content/eq98.tif"/>
