Answer
Fill the blanks with
distributive,
$x^{2}+5x+7$,
$2x^{2}$
Work Step by Step
We use the distributive property, $A(B+C+D)=AB+AC+AD$
by multiplying each term of the polynomial $x^{2}+5x+7$ with the monomial in front of the parentheses, $2x^{2}.$
$2x^{2}(x^{2}+5x+7)=2x^{2}\cdot(x^{2})+2x^{2}\cdot(5x)+2x^{2}\cdot(7)$,
which simplifies to
$=2x^{4}+10x^{3}+14x^{2}$
