Factorize 6n^2-n-2.if the factors are measures of sides of a rectangle then find the sum of areas of four sqares drawn on the sides of the rectangle
Answers
Given : 6n² - n - 2 factors are measures of sides of a rectangle
To find : sum of areas of four sqares drawn on the sides of the rectangle
Solution:
6n² - n - 2
= 6n² - 4n + 3n - 2
= 2n(3n - 2) + 1(3n - 2)
= (2n + 1)(3n - 2)
Examples of Side of Rectangles
are 2n + 1 & 3n-2 area Sum of area of 4 Sqaures
n = 1 3 1 3 2(3² + 1²) = 20
n =2 5 4 20 2(5² + 4²) = 82
n =3 7 7 49 2(7² + 7²) = 196
sum of areas of four sqares drawn on the sides of the rectangle
= 2 (2n + 1)² + 2(3n - 2)²
= 2 ( 4n² + 4n + 1) + 2 (9n² -12n + 4)
= 2( 4n² + 4n + 1 + 9n² - 12n + 4)
= 2( 13n² - 8n + 5 )
= 26n² - 16n + 10
26n² - 16n + 10 is the area of four squares drawn on the sides of the rectangle
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