Question

2y^2+ 10y + 12.5 - 24.5z^2 - 18 +42z

Answer 1

Given : 2y²+ 10y + 12.5 - 24.5z² - 18 +42z

To find : Factorize

Solution:

2y²+ 10y + 12.5 - 24.5z^2 - 18 +42z

multiply & divide by 2

= (1/2)2( 2y²+ 10y + 12.5 - 24.5z² - 18 +42z )

= (1/2) (4y²+ 20y + 25 - 49z²- 36 +84z)

=(1/2) (4y²+ 20y + 25 - (49z² + 36 -84z))

=(1/2) ((2y)²+ 2.2y.5y + 5² - ((7z)² + 6² -2z.7.6))

= (1/2) ((2y+5)²- (7z-6)²)

using a² - b²

= (1/2) ( 2y + 5 + 7z - 6) (2y + 5 -(7z - 6) )

= (1/2) ( 2y + 7z - 1) (2y -7z + 11 )

2y²+ 10y + 12.5 - 24.5z² - 18 +42z =  (1/2) ( 2y + 7z - 1) (2y -7z + 11 )

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