Question

(2m-5)^2-2m+3=4(m+1)^2-16

Answer 1

$\: \: \: \: (2m - 5) ^{2} - 2m + 3 = 4(m + 1) ^{2} - 16 \\ = > 4 {m}^{2} + 25 - 20m - 2m + 3 = 4m ^{2} + 4 + 8m - 16 \\ 4m ^{2} \: will \: be \: cut \: from \: both \: the \: sides \\ = > 25 - 22m + 3 = 8m - 12 \\ = > 25 + 12 + 3 = 30m \\ = > m = 4/3.$

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Answer 2

Answer:

Required value of the variable m is - 4 / 3

Step-by-step explanation:

= >  ( 2m - 5 )^2 - 2m + 3 = 4( m + 1 )^2 - 16

From factorization, we know that the value of the ( a + b )^2 is a^2 + b^2 + 2ab and the value of ( a - b )^2 is a^2 + b^2 - 2ab

= > ( 2m )^2 + ( 5 )^2 - 2( 2m x 5 ) - 2m + 3 = 4[ ( m )^2 + ( 1 )^2 + 2( m x 1 ) ] - 16

= >  4m^2 + 25 - 20m - 2m + 3 = 4[ m^2 + 1 + 2m ] - 16

= >  4m^2 - 22m + 3 + 25 = 4m^2 + 4 + 8m - 16

= >  4m^2 - 22m + 28 = 4m^2 + 8m - 16 + 4

= >  4m^2 - 22m + 28 = 4m^2 + 8m - 12

= >  4m^2 - 22m + 28 - 4m^2 - 8m + 12 = 0

= >  4m^2 - 4m^2 - 22m - 8m + 28 + 12 = 0

= >  30m + 40 = 0

= >  30m = - 40

= >  m = - 40 / 30

= >  m = - 4 / 3