$5x$; $3$; like
Work Step by Step
RECALL: For any real numbers a, b, c, d, and e, the distributive property states that $(a+b)(c+d+e) = a(c+d+e) + b(c+d+e).$ Thus, to multiply $(5x+3)(x^2+8x+7)$, use the distributive property to obtain $5x(x^2+8x+7) + 3(x^2+8x+7) \\=5x^3+40x^2+35x+3x^2+24x+21.$ To simplify the result, you have to combine like terms. Therefore. the missing expressions (in order) in the given statement are $5x$, $3$, and like.