Question

Factorise 4x²+9y²-25z²+12xy

Answer 1

HI,
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Fist step:-→ 4x² + 9y² - 25z² + 12xy

2nd step→(2x)² + (3y)² - (5z)² + 2(2x)(3y)

3rd step:-→(2x)² + 2(2x)(3y) + (3y)² - (5z)² 

4th step:-→(2x + 3y)² - (5z)²         

 Final answer:-∴(2x + 3y + 5z)(2x + 3y - 5z) ======================================
Now,
We can't factor it further...
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:-)

Answer 2

Solution:

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Given & To Find:

Factorize:

 4x²+9y²-25z²+12xy
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we know the two identites (By using these we are going to solve this problem),

(a + b)² = a² + 2ab + b²,

a² - b² = (a + b)(a - b),.

Going back to the expression,

=> 4x² + 9y² - 25z² + 12xy

=> (2x)² + (3y)² - (5z)² + 2(2x)(3y)

=> (2x)² + 2(2x)(3y) + (3y)² - (5z)²

=>(2x + 3y)² - (5z)²        (By using (a + b)² identity)
 
=> (2x + 3y + 5z)(2x + 3y - 5z),. (By using a² - b² identity),.

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                                  Hope it Helps !!