Question

factorise 3(x+2y)^2+5(x+2y)+2​

Answer 1

Answer ::

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Step-by-step explanation:

$\underline{\underline{{\purple{\sf Given}}}}$

☞$\sf{3(x+2y)^2+5(x+2y)+2=0}$

$\ \implies$$\sf{3(x^2+4y^2+4xy)+5x+10y+2=0}$

$\ \implies$$\sf{3x^2+12y^2+12xy+5x+10y+2=0}$

$\ \implies$$\sf{ie 3(x+2y)^2+5(x+2y)+2=0}$

☞$\bf{consider\: the \: value \:of \: (x+2y)=p}$

$\ \implies$$\sf{3p^2+5p+2=0}$

$\ \implies$$\sf{3p^2+6p-p+2=0}$

$\ \implies$$\sf{3p(p+2)-1(p+2)}$

$\ \implies$$\sf{(3p-1)(p+2)=0}$

$\ \implies$$\sf{p=\dfrac{1}{3} and p=-2}$

☞$\bf{now \: put \: p \: value \: in the values }$

$\ \implies$$\sf{3(x+2y)-1 =0 and x+2y=2}$

$\ \implies$$\sf{3x+4y-1=0 and x+2y=2}$

☞$\bf{Now \: solve \: linear equations }$^ω^^ω^^ω^

$\ \implies$ $\sf{3x+4y=1.......(1)}$

$\ \implies$ $\sf{x+2y=2.......(2)}$

☞$\bf{multiply in equations (2)by 2 }$^ω^

$\ \implies$$\sf{3x+4y=1}$

$\ \implies$$\sf{2x+4y=4}$

$\ \implies$$\bf{x=-3..........(3) }$

☞$\sf{now \:put \:the \:value\ :of \: X =-3\:in \:equation (2)}$^ω^^ω^

$\ \implies$$\sf{2(-3)+4y=4}$

$\ \implies$$\sf{-6+4y=4}$

$\ \implies$$\sf{-6+4y-4=0}$

$\ \implies$$\sf{4y=10}$

$\ \implies$$\bf{y=\dfrac{10}{4}=\dfrac{5}{2}}$

$\ \implies$$\sf{x=-3 and y=\dfrac{5}{2}}$

$\bold{\purple{\fbox{\red{Please thank it}}}}$ʕ•ε•ʔ

Answer 2

Answer:

answer for the given problem is given