Solve (-r^2+3r-7)(r^2-7)

$$( - r ^ { 2 } + 3 r - 7 ) ( r ^ { 2 } - 7 )$$

Expand

$$49-21r+3r^{3}-r^{4}$$

Solution Steps

Use the distributive property to multiply -r^{2}+3r-7 by r^{2}-7.

$$\left(-r^{2}\right)r^{2}-7\left(-r^{2}\right)+3r^{3}-21r-7r^{2}+49$$

Multiply -7 and -1 to get 7.

$$\left(-r^{2}\right)r^{2}+7r^{2}+3r^{3}-21r-7r^{2}+49$$

Combine 7r^{2} and -7r^{2} to get 0.

$$\left(-r^{2}\right)r^{2}+3r^{3}-21r+49$$

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

$$-r^{4}+3r^{3}-21r+49$$

Evaluate

$$\left(-r^{2}+3r-7\right)\left(r^{2}-7\right)$$

Solution Steps

Use the distributive property to multiply -r^{2}+3r-7 by r^{2}-7.

$$\left(-r^{2}\right)r^{2}-7\left(-r^{2}\right)+3r^{3}-21r-7r^{2}+49$$

Multiply -7 and -1 to get 7.

$$\left(-r^{2}\right)r^{2}+7r^{2}+3r^{3}-21r-7r^{2}+49$$

Combine 7r^{2} and -7r^{2} to get 0.

$$\left(-r^{2}\right)r^{2}+3r^{3}-21r+49$$

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

$$-r^{4}+3r^{3}-21r+49$$