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\left(15x^{2}-5x+3x-1\right)\left(x+3\right)
Apply the distributive property by multiplying each term of 5x+1 by each term of 3x-1.
\left(15x^{2}-2x-1\right)\left(x+3\right)
Combine -5x and 3x to get -2x.
15x^{3}+45x^{2}-2x^{2}-6x-x-3
Apply the distributive property by multiplying each term of 15x^{2}-2x-1 by each term of x+3.
15x^{3}+43x^{2}-6x-x-3
Combine 45x^{2} and -2x^{2} to get 43x^{2}.
15x^{3}+43x^{2}-7x-3
Combine -6x and -x to get -7x.
\left(15x^{2}-5x+3x-1\right)\left(x+3\right)
Apply the distributive property by multiplying each term of 5x+1 by each term of 3x-1.
\left(15x^{2}-2x-1\right)\left(x+3\right)
Combine -5x and 3x to get -2x.
15x^{3}+45x^{2}-2x^{2}-6x-x-3
Apply the distributive property by multiplying each term of 15x^{2}-2x-1 by each term of x+3.
15x^{3}+43x^{2}-6x-x-3
Combine 45x^{2} and -2x^{2} to get 43x^{2}.
15x^{3}+43x^{2}-7x-3
Combine -6x and -x to get -7x.