Question

factorise: 49(a-b)^2-25(a+b)^2

Answer 1

$49(a-b)^{2} - 25(a+b)^{2} \\= 7^{2}(a-b)^{2} - 5^{2}(a+b)^{2} \\= [7(a-b)]^{2} - [5(a+b)]^{2} \\= (7a-7b)^{2} - (5a+5b)^{2} \\= [(7a-7b)+(5a+5b)][(7a-7b)-(5a+5b)]$

$\blue {( By \: Algebraic \:Identity )}$

$\boxed { \pink { x^{2} - y^{2} = ( x + y )( x - y ) }}$

$= [7a-7b+5a+5b][7a-7b-5a-5b] \\= ( 7a+5a-7b+5b)(7a-5a-7b-5b)\\= (12a-2b)(2a-12b)\\= [2(6a-b)][ 2(a-6b)] \\= 4(6a-b)(a-6b)$

Therefore.,

$\red{ Factors \:of \:49(a-b)^{2} - 25(a+b)^{2}}\\\green {= 4(6a-b)(a-6b)}$

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Answer 2

Answer:

49(a-b)^2-25(a+b)^2