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\left(x^{2}+5x+3x+15\right)x
Apply the distributive property by multiplying each term of x+3 by each term of x+5.
\left(x^{2}+8x+15\right)x
Combine 5x and 3x to get 8x.
x^{3}+8x^{2}+15x
Use the distributive property to multiply x^{2}+8x+15 by x.
\left(x^{2}+5x+3x+15\right)x
Apply the distributive property by multiplying each term of x+3 by each term of x+5.
\left(x^{2}+8x+15\right)x
Combine 5x and 3x to get 8x.
x^{3}+8x^{2}+15x
Use the distributive property to multiply x^{2}+8x+15 by x.