Solve (r^2-8r-2)(-r^2+3r-1)

$$( r ^ { 2 } - 8 r - 2 ) ( - r ^ { 2 } + 3 r - 1 )$$

Evaluate

$$\left(-r^{2}+3r-1\right)\left(r^{2}-8r-2\right)$$

Solution Steps

Use the distributive property to multiply r^{2}-8r-2 by -r^{2}+3r-1 and combine like terms.

$$r^{2}\left(-r^{2}\right)+3r^{3}-25r^{2}-8r\left(-r^{2}\right)+2r-2\left(-r^{2}\right)+2$$

Multiply -8 and -1 to get 8.

$$r^{2}\left(-r^{2}\right)+3r^{3}-25r^{2}+8rr^{2}+2r-2\left(-r^{2}\right)+2$$

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

$$r^{2}\left(-r^{2}\right)+3r^{3}-25r^{2}+8r^{3}+2r-2\left(-r^{2}\right)+2$$

Combine 3r^{3} and 8r^{3} to get 11r^{3}.

$$r^{2}\left(-r^{2}\right)+11r^{3}-25r^{2}+2r-2\left(-r^{2}\right)+2$$

Multiply -2 and -1 to get 2.

$$r^{2}\left(-r^{2}\right)+11r^{3}-25r^{2}+2r+2r^{2}+2$$

Combine -25r^{2} and 2r^{2} to get -23r^{2}.

$$r^{2}\left(-r^{2}\right)+11r^{3}-23r^{2}+2r+2$$

To multiply powers of the same base, add their exponents. Add 2 and 2 to get 4.

$$r^{4}\left(-1\right)+11r^{3}-23r^{2}+2r+2$$

Expand

$$2+2r-23r^{2}+11r^{3}-r^{4}$$

Solution Steps

Use the distributive property to multiply r^{2}-8r-2 by -r^{2}+3r-1 and combine like terms.

$$r^{2}\left(-r^{2}\right)+3r^{3}-25r^{2}-8r\left(-r^{2}\right)+2r-2\left(-r^{2}\right)+2$$

Multiply -8 and -1 to get 8.

$$r^{2}\left(-r^{2}\right)+3r^{3}-25r^{2}+8rr^{2}+2r-2\left(-r^{2}\right)+2$$

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

$$r^{2}\left(-r^{2}\right)+3r^{3}-25r^{2}+8r^{3}+2r-2\left(-r^{2}\right)+2$$

Combine 3r^{3} and 8r^{3} to get 11r^{3}.

$$r^{2}\left(-r^{2}\right)+11r^{3}-25r^{2}+2r-2\left(-r^{2}\right)+2$$

Multiply -2 and -1 to get 2.

$$r^{2}\left(-r^{2}\right)+11r^{3}-25r^{2}+2r+2r^{2}+2$$

Combine -25r^{2} and 2r^{2} to get -23r^{2}.

$$r^{2}\left(-r^{2}\right)+11r^{3}-23r^{2}+2r+2$$

To multiply powers of the same base, add their exponents. Add 2 and 2 to get 4.

$$r^{4}\left(-1\right)+11r^{3}-23r^{2}+2r+2$$