given quadratic equation is 3x^2+10xy+8y^2
we can solve this problem splitting the middle term,
we cam multiply the first term and last term then ,24x^2y^2
we can rewrite the product equal to the middle term,(6xy)(4xy)=6xy+4xy
= 3x^2+4xy+6xy+8y^2
=x(3x+4y)+2y(3x+4y)
=(3x+4y)(x+2y),
if you want to continue the problem and has to find x,y values
we equalize the two factors with zero then,3x+4y=0----(1),x+2y=0-----(2)
x+2y=0
x=-2y
now we can put the x value in equation in(1) then
3(-2y)+4y=0
-6y+4y=0=>-2y=0=> y=0 ,now x=0
3x2 +10xy +8y2
solution:-
Those types of question first we see to solve it by formula if that not solve with formula then we solve it by MIDDLE TERM BREAK
BY MIDDLE TERM BREAK
for middle term break first we multiply first and last term we get 3x² x (+8y²) = 24x²y²
now we break the middle term in such a manner that if we multiply we get +24x²y² and add or subtract we return get 10xy
3x^{2} +10xy +8y^{2}
3x^{2 }+ 6xy + 4xy + 8y²
take common in each pair (in common the term should b lowest power variable)
3x(x + 2y) + 4y(x + 2y)
again common
(x + 2y)(3x + 4y)
If you find the values of x and y then equalise it with zero.