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?

Question

Darwin Garrett

Mathematics

12 April, 10:16

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?

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Jacquelyn Oconnell · 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.