Explore a diverse range of topics and get answers from knowledgeable individuals on IDNLearn.com. Explore thousands of verified answers from experts and find the solutions you need, no matter the topic.
From the given problem :
[tex]\frac{x^2y^4}{x^2+11x+28}\times\frac{x^2+2x-8}{x^6y^3}[/tex]x^2 + 11x + 28 can be factored as, you need to think of two numbers that has a product of 28 and a sum of 11. In this case it's 7 and 4 :
(x + 7)(x + 4)
and x^2 + 2x - 8 can be factored as, you need to think of two numbers that has a product of -8 and a sum of 2. In this case it's 4 and -2 :
(x + 4)(x - 2)
So the expression will be :
[tex]\frac{x^2y^4}{(x+7)(x+4)}\times\frac{(x+4)(x-2)}{x^6y^3}[/tex]The term (x+4) will be cancelled out
[tex]\frac{x^2y^4(x-2)}{x^6y^3(x+7)}[/tex]Simplify further and the answer is :
[tex]\frac{y(x-2)}{x^4(x+7)}[/tex]