Simplify : (3.5a - 1.5b)^2 - (1.5a- 3.5b)^2

1.	Simplify : (3.5a - 1.5b)^2 - (1.5a- 3.5b)^2
Answer» Answer: (3.5 a - 1.5 b ) ^ 2 - ( 1.5 a - 3.5 b ) ^ 2 { I am solving (3.5 a - 1.5 b ) ^ 2 by 2 nd equation and again ( 1.5 a - 3.5 b ) ^ 2 by 2 nd equation } Step-by-step explanation: ( a - b ) ^ 2 = a^2 + b ^2 - 2ab here a = 3.5 a , b = 1.5 b also , a = 1.5 a , b = 3.5 b (3.5 a - 1.5 b ) ^ 2 - ( 1.5 a - 3.5 b ) ^ 2 = [ ( 3.5 a ) ^2 + ( 1 .5 b )^ 2 - 2 ( 3.5 a) ( 1. 5 b) ] - [ ( 1 .5 a )^ 2 + ( 3.5 b ) ^2 - 2 ( 1. 5 a ) ( 3.5 b) ] = 12.25 a^ 2 + 2. 25 b ^ 2 - 10.5 AB - 2.25 a ^2+ 1 2. 25 b ^ 2+ 10.25 ab =[ 12.25 a^ 2 - 2.25 a ^2] +[ 2. 25 b ^ 2 + 12. 25 b ^ 2][ - 10.5 ab + 10.25 ab] = 10 a^2 + 10 b^2 + 0 = 10 a^2 + 10 b^2

Answer»

Answer:

(3.5 a - 1.5 b ) ^ 2 - ( 1.5 a - 3.5 b ) ^ 2

{ I am solving (3.5 a - 1.5 b ) ^ 2 by 2 nd equation and again ( 1.5 a - 3.5 b ) ^ 2 by 2 nd equation }

Step-by-step explanation:

( a - b ) ^ 2 = a^2 + b ^2 - 2ab

here a = 3.5 a , b = 1.5 b

also , a = 1.5 a , b = 3.5 b

(3.5 a - 1.5 b ) ^ 2 - ( 1.5 a - 3.5 b ) ^ 2

= [ ( 3.5 a ) ^2 + ( 1 .5 b )^ 2 - 2 ( 3.5 a) ( 1. 5 b) ] - [ ( 1 .5 a )^ 2 + ( 3.5 b ) ^2 -

2 ( 1. 5 a ) ( 3.5 b) ]

= 12.25 a^ 2 + 2. 25 b ^ 2 - 10.5 AB - 2.25 a ^2+ 1 2. 25 b ^ 2+ 10.25 ab

=[ 12.25 a^ 2 - 2.25 a ^2] +[ 2. 25 b ^ 2 + 12. 25 b ^ 2][ - 10.5 ab + 10.25 ab]

= 10 a^2 + 10 b^2 + 0

= 10 a^2 + 10 b^2

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