Question

9x² - 4(x+y)² need to factories

Answer 1

HELLO FRIEND HERE IS YOUR ANSWER,,,,,

Given equation needed to be factorised,,

$= > 9 {x}^{2} - 4 {(x + y)}^{2}$

Now,,,

$3^2 x^2 - 2^2 (x + y)^2$

By applying the following exponential rule,,,

$= > {a}^{m} \times {b}^{m} \: = \: {(ab)}^{m}$

Therefore,,,,

$= > (3 {x}^{2} ) - { {2}^{2} \: (x + y)}^{2}$

$= > (3 {x}^{2} ) - {(2(x + y))}^{2}$

By applying the following difference rule of two square formulae

$= > {x}^{2} - {y}^{2} = (x + y) \times (x - y)$

Therefore,,,,

$= > (3x + 2(x + y)) \times (3x - 2(x + y)) \\ \\ \\ = > (3x + 2x + 2y) \times (3x - 2x + 2y) \\ \\ \\ = > (5x + 2y) \times (x - 2y) \\ \\ or \\ \\ = > (5x + 2y)(x - 2y)$

Which is the required solution for this type of query.

HOPE IT HELPS YOU AND CLEARS THE DOUBTS FOR ADVANCED FACTORISATION!!!!!