Exercise - 6.2
1. Find the square of the following numbers
by using distributive property.
(i) 32 (ii) 35 (iii) 86 (iv) 93
(v) 71 (vi) 46
2. Write a Pythagorean triplet whose one
member is.
(i) 6 (ii) 14 (iii) 16 (iv) 18
*PLEASE USE DISTRIBUTIVE PROPERTY IN THE 1 QUESTION WITH EXPLANATION*
Answers
Hey buddy here is your answer
Step-by-step explanation:
Q1) I) 32^2=(30+2)^2 (Distributive)
using (a+b) ^2= a^2 + b^2 + 2ab
a=30, b= 2
30^2+ 2^2 + 2*30*2
=900+4+120
= 1024
Q1) ii) 35^2=(30+5)^2 (Distributive)
using (a+b) ^2= a^2 + b^2 + 2ab
a=30, b= 5
30^2+ 5^2 + 2*30*5
900+25+300
1225
Q1) iii) 86^2= (80+6)^2 (Distributive)
using (a+b) ^2= a^2 + b^2 + 2ab
(80+6)^2= 80^2 + 6^2 +2*80*6
6400+36+960
7496
similarly other parts
Q2 Pythagorean triplets are 2m, m^2+1, m^2-1
i) lets take 2m=6
m=3
m^2+1= 3^2+1= 9+1= 10
m^2-1= 3^2-1= 9-1= 8
the triplet is 6,10,8
ii) let's take 2m = 14
m= 7
m^2+1= 7^2+1=49+1= 50
m^2-1= 7^2-1= 49-1= 48
the triplet is 14,50,48
iii) let's take 2m = 16
m= 8
m^2+1= 8^2+1=64+1= 65
m^2-1= 8^2-1= 64-1= 63
the triplet is 16,63,65
iv) let's take 2m = 18
m= 9
m^2+1= 9^2+1= 81+1= 82
m^2-1= 8^2-1= 81-1= 80
the triplet is 18,82,80
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Demon 445
Given : Numbers
(i) 32 (ii) 35 (iii) 86 (iv) 93 (v) 71 (vi) 46
To Find : Evaluate Square of numbers using Distributive property
Solution:
Square of 46
= 46²
= 46 × 46
= 46 × (50 - 4)
Distributive property
a × ( b ± c) = a× b ± a × c
= 46 × 50 - 46 × 4
= 2300 - 184
= 2116
Square of 46 = 2116
Similarly
32² = 1024
35² = 1225
86² = 7396
71² = 5041
Pythagorean triplet ( a , b , c)
c² = a² + b² c > a , b
(6 , 8 , 10)
(12 , 16 , 20)
(18 , 24 , 30)
(14 , 48 , 50)
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