#### Answer

$5x$;
$3$;
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.