ABSTRACT
RECALL arithmetical problems that you learned to tackle earlier on in your education: solving linear equations ax + b = 0 and quadratic equations ax 2 + bx + c = 0, factoring terms like a 2 − b 2 = (a + b)(a − b) or a 3 + b 3 = (a + b)(a 2 − ab + b 2), finding product expansions like (x + y)3 = x 3 + 3x 2 y + 3xy 2 + y 3, and so on. All these problems involve the two basic operations of addition and multiplication, and arithmetic can be characterized as the art of handling these two operations. For example, the quadratic equation ax 2 + bx + c = 0 is essentially solved by simply rewriting it in the form a ( x + b 2 a ) 2 + c − b 2 4 a = 0 https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315136554/b1e97aa6-f63a-4d22-960d-a98dde0e94f9/content/eq1.tif"/> or ( x + b 2 a ) 2 = b 2 − 4 a c 4 a 2 https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315136554/b1e97aa6-f63a-4d22-960d-a98dde0e94f9/content/eq2.tif"/> .
