Question

please help me and i promise i will mark you as brainliest factor it by step by step 3+11(x+y)-4(x+y)^{2}

Answer 1

Answer:

-(4(x+y)+1)(x+y-3)

Step-by-step explanation:

factor out the common term -1 first to get

$-\left(4\left(x+y\right)^2-11\left(x+y\right)-3\right)$

(take out the -1 for now, we'll add it back later)

$\: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)$$\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)$

$\mathrm{Factor\:out\:}-3\mathrm{\:from\:}-12\left(x+y\right)-3\mathrm{:\quad }-3\left(4\left(x+y\right)+1\right)$$\mathrm{Factor\:out\:common\:term\:}4\left(x+y\right)+1$

$\left(4\left(x+y\right)+1\right)\left(\left(x+y\right)-3\right)$

add back the -1 from the first step

$-\left(4\left(x+y\right)+1\right)\left(\left(x+y\right)-3\right)$

Refine the equation:

$-\left(x+y-3\right)\left(4\left(x+y\right)+1\right)$

Answer 2

Answer:

- ( x + y - 3 )( 4x + 4y + 1 )

Step-by-step explanation:

Consider the steps below;

$3+11\left(x+y\right)-4\left(x+y\right)^2,\\\\\,-\left(4\left(x+y\right)^2-11\left(x+y\right)-3\right)\\\\4\left(x+y\right)^2+\left(x+y\right) = 4\left(x+y\right)\left(x+y\right)+\left(x+y\right)\\ = \left(x+y\right)\left(4\left(x+y\right)+1\right),\\-12\left(x+y\right)-3 = -3\cdot \:4\left(x+y\right)-3 = -3\left(4\left(x+y\right)+1\right),\\\left(x+y\right)\left(4\left(x+y\right)+1\right)-3\left(4\left(x+y\right)+1\right),$

$Refine, -\left(x+y-3\right)\left(4x + 4y+1\right)$

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 )