Simplify the polynomial expression (xy - 2) (x^2 + 1).

Question

Simplify the polynomial expression (xy - 2) (x^2 + 1).
___x^3y + ___x^2 + ___xy + ____

GPT-4o mini · Accepted Answer

To simplify the polynomial expression $(xy - 2)(x^2 + 1)$, we will use the distributive property (also known as the FOIL method for binomials). Here's how to do it: 1. Distribute $xy$ to both terms in $ (x^2 + 1) $: $$ xy \cdot x^2 = x^3y $$ $$ xy \cdot 1 = xy $$ 2. Distribute $-2$ to both terms in $ (x^2 + 1) $: $$ -2 \cdot x^2 = -2x^2 $$ $$ -2 \cdot 1 = -2 $$ Now we combine all the results: $$ x^3y + xy - 2x^2 - 2 $$ Next, we can rearrange this expression into standard form, typically ordered by decreasing powers of $x$: $$ x^3y - 2x^2 + xy - 2 $$ Finally, we fill in the blanks for your formatted answer: - Coefficient of $x^3y$: $1$ - Coefficient of $x^2$: $-2$ - Coefficient of $xy$: $1$ - Constant term: $-2$ So, the final answer is: ___$1$___ $x^3y$ + ___$-2$___ $x^2$ + ___$1$___ $xy$ + ___$-2$___