Solve (r+5)(r-5)(r^2+25)?

$$( r + 5 ) ( r - 5 ) ( r ^ { 2 } + 25 ) ?$$

Evaluate

$$r^{4}-625$$

Solution Steps

Use the distributive property to multiply r+5 by r-5 and combine like terms.

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

Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. Square 25.

$$\left(r^{2}\right)^{2}-625$$

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

$$r^{4}-625$$

Expand

$$r^{4}-625$$

Solution Steps

Use the distributive property to multiply r+5 by r-5 and combine like terms.

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

Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. Square 25.

$$\left(r^{2}\right)^{2}-625$$

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

$$r^{4}-625$$