Question

(4x+5)²-(2y+3)², Factorize the given equation.

Answer 1

$(4x + 5) {}^{2} - (2y + 3) {}^{2} \\ = (4x + 5 + 2 y + 3)(4x + 5 - 2y - 3) \\ = (4x + 2y + 8)(4x - 2y + 2)$

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Answer 2

Answer:

( 4x+2y+8 )( 4x-2y+2 )

Or

4( 2x+y+4 )( 2x-y+1 )

Step-by-step explanation:

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We know the algebraic identity:

m² - n² = ( m + n )( m - n )

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Here ,

( 4x + 5 )² - ( 2y + 3 )²

= [4x+5+(2y+3)][4x+5-(2y+3)]

= ( 4x+5+2y+3 )( 4x+5-2y-3 )

= ( 4x+2y+8 )( 4x-2y+2 )

Or

= 4( 2x+y+4)( 2x-y+1 )

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