8. multiply the polynomials.
(xy - 1) (xy + 6) (xy - 8)
enter your answer.
check answer

Question

Accepted Answer

# Explanation:
## Step1: Multiply first two polynomials
We use the distributive property (FOIL method) to multiply $(xy - 1)(xy + 6)$.
$$
\begin{align*}
(xy - 1)(xy + 6)&=xy\times xy+xy\times6 - 1\times xy-1\times6\
&=x^{2}y^{2}+6xy - xy - 6\
&=x^{2}y^{2}+5xy - 6
\end{align*}
$$
## Step2: Multiply the result with the third polynomial
Now we multiply $(x^{2}y^{2}+5xy - 6)$ with $(xy - 8)$ using the distributive property.
$$
\begin{align*}
&(x^{2}y^{2}+5xy - 6)(xy - 8)\
=&x^{2}y^{2}\times xy+x^{2}y^{2}\times(- 8)+5xy\times xy+5xy\times(-8)-6\times xy-6\times(-8)\
=&x^{3}y^{3}-8x^{2}y^{2}+5x^{2}y^{2}-40xy - 6xy + 48\
=&x^{3}y^{3}+(-8x^{2}y^{2}+5x^{2}y^{2})+(-40xy-6xy)+48\
=&x^{3}y^{3}-3x^{2}y^{2}-46xy + 48
\end{align*}
$$

# Answer:
$x^{3}y^{3}-3x^{2}y^{2}-46xy + 48$

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Step1: Multiply first two polynomials

Step2: Multiply the result with the third polynomial

Answer: