Question

step 2: multiply rows & columns
$(x - 3)(2x^2 - x + 5)$
$2x^2$ $-x$ $+5$
$x$ $2x^3$ $-x^2$ $5x$
$-3$ $-6$ $3x$ $-15$
pro tip: type \x2\ to get \x2\
check exponents (small numbers).
$-3 \times 2$

Explanation:

Step1: Multiply -3 by $2x^2$

$(-3) \times 2x^2 = -6x^2$

Step2: List all expanded terms

$2x^3 - x^2 + 5x - 6x^2 + 3x - 15$

Step3: Combine like terms

$2x^3 + (-x^2 -6x^2) + (5x + 3x) -15 = 2x^3 -7x^2 +8x -15$

Answer:

The missing term in the red box is $\boldsymbol{-6x^2}$, and the fully expanded and simplified expression is $2x^3 -7x^2 +8x -15$