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4\left(3x^{2}+8xy+5y^{2}\right)
Factor out 4.
3x^{2}+8yx+5y^{2}
Consider 3x^{2}+8xy+5y^{2}. Consider 3x^{2}+8xy+5y^{2} as a polynomial over variable x.
\left(3x+5y\right)\left(x+y\right)
Find one factor of the form kx^{m}+n, where kx^{m} divides the monomial with the highest power 3x^{2} and n divides the constant factor 5y^{2}. One such factor is 3x+5y. Factor the polynomial by dividing it by this factor.
4\left(3x+5y\right)\left(x+y\right)
Rewrite the complete factored expression.