Question

Factorise: 12(y^2+7y)^2-8(y^2+7y)(2y-1)-15(2y-1)^2 Please tell the answer in detail with the name of the property listed

Answer 1

Step-by-step explanation:

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Answer 2

$Given \: 12(y^2+7y)^2-8(y^2+7y)(2y-1)-15(2y-1)^2$

$Let \: a = (y^{2} + 7y) , \:and \: b = (2y-1)$

\* Rewrite the Expression, we get *\

$= 12a^{2} - 8ab- 15b^{2}$

\* Splitting the middle term,we get *\

$= 12a^{2} + 18ab - 10ab - 15b^{2} \\= 6a( 2a + 3b) - 5b(2a + 3b) \\= (2a + 3b)( 6a - 5b ) \\= [ 2(y^{2}+7y) + 3(2y-1) ] [ 6(y^{2}+7y) - 5(2y-1) ] \\= (2y^{2} + 14y +6y - 3) (6y^{2}+42y-10y+5) \\= (2y^{2}+20y-3)(6y^{2}+32y+5)$

Therefore.,

$\red{ Factors \:of \: 12(y^2+7y)^2-8(y^2+7y)(2y-1)-15(2y-1)^2}\\\green{=(2y^{2}+20y-3)(6y^{2}+32y+5)}$

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