Question

A student is asked to calculate the value of 212 − 132 using the identity x2 − y2 = (x − y)(x + y). The student's steps are shown below. Step 1: 212 − 132 = (a − b)(a + b) Step 2: = (c)(d) Step 3: = (8)(30) + 8(4) Step 4: = 240 + 32 Step 5: = 272 What are the values of a, b, c, and d?

Answer 1

(c)*(d)=8*30+8*4=8*34,=>
c=8
d=34
a+b>a-b, =>a+b=d, a-b=c; =>
{a+b=34
{a-b=8, =>a=b+8 ;
(b+8)+b=34
2b=34-8
b=13
a=13+8=21

Answer: a=21; b=13; c=8; d=34.