Respuesta :
Answer:
-(4(x+y)+1)(x+y-3)
Step-by-step explanation:
factor out the common term -1 first to get
[tex]-\left(4\left(x+y\right)^2-11\left(x+y\right)-3\right)[/tex]
(take out the -1 for now, we'll add it back later)
[tex]\:4\left(x+y\right)^2-11\left(x+y\right)-3:\quad \left(4\left(x+y\right)+1\right)\left(\left(x+y\right)-3\right)[/tex][tex]\mathrm{Factor\:out\:}\left(x+y\right)\mathrm{\:from\:}4\left(x+y\right)^2+\left(x+y\right)\mathrm{:\quad }\left(x+y\right)\left(4\left(x+y\right)+1\right)[/tex]
[tex]\mathrm{Factor\:out\:}-3\mathrm{\:from\:}-12\left(x+y\right)-3\mathrm{:\quad }-3\left(4\left(x+y\right)+1\right)[/tex][tex]\mathrm{Factor\:out\:common\:term\:}4\left(x+y\right)+1[/tex]
[tex]\left(4\left(x+y\right)+1\right)\left(\left(x+y\right)-3\right)[/tex]
add back the -1 from the first step
[tex]-\left(4\left(x+y\right)+1\right)\left(\left(x+y\right)-3\right)[/tex]
Refine the equation:
[tex]-\left(x+y-3\right)\left(4\left(x+y\right)+1\right)[/tex]
Answer:
- ( x + y - 3 )( 4x + 4y + 1 )
Step-by-step explanation:
Consider the steps below;
[tex]3+11\left(x+y\right)-4\left(x+y\right)^2,\\\\\,-\left(4\left(x+y\right)^2-11\left(x+y\right)-3\right)\\\\4\left(x+y\right)^2+\left(x+y\right) = 4\left(x+y\right)\left(x+y\right)+\left(x+y\right)\\ = \left(x+y\right)\left(4\left(x+y\right)+1\right),\\-12\left(x+y\right)-3 = -3\cdot \:4\left(x+y\right)-3 = -3\left(4\left(x+y\right)+1\right),\\\left(x+y\right)\left(4\left(x+y\right)+1\right)-3\left(4\left(x+y\right)+1\right),\\[/tex]
[tex]Refine, -\left(x+y-3\right)\left(4x + 4y+1\right)[/tex]
To derive the second step, I factored out common term 1, receiving the expression - ( 4( x + y )^2 - 11( x + y ) - 3 ). Breaking this expression into groups, I took one part in ( ) and simplified it further, doing so for the second part as well. Refining the expression I received the following expression;
Solution ⇒ - ( x + y - 3 )( 4x + 4y + 1 )
