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2x+8x^{2}+12xy+5+20x+30y-6x\left(x+y\right)
Apply the distributive property by multiplying each term of 2x+5 by each term of 1+4x+6y.
22x+8x^{2}+12xy+5+30y-6x\left(x+y\right)
Combine 2x and 20x to get 22x.
22x+8x^{2}+12xy+5+30y-6x^{2}-6xy
Use the distributive property to multiply -6x by x+y.
22x+2x^{2}+12xy+5+30y-6xy
Combine 8x^{2} and -6x^{2} to get 2x^{2}.
22x+2x^{2}+6xy+5+30y
Combine 12xy and -6xy to get 6xy.
2x+8x^{2}+12xy+5+20x+30y-6x\left(x+y\right)
Apply the distributive property by multiplying each term of 2x+5 by each term of 1+4x+6y.
22x+8x^{2}+12xy+5+30y-6x\left(x+y\right)
Combine 2x and 20x to get 22x.
22x+8x^{2}+12xy+5+30y-6x^{2}-6xy
Use the distributive property to multiply -6x by x+y.
22x+2x^{2}+12xy+5+30y-6xy
Combine 8x^{2} and -6x^{2} to get 2x^{2}.
22x+2x^{2}+6xy+5+30y
Combine 12xy and -6xy to get 6xy.