Solve (-r^2-(r-R)^2)

$$( - r ^ { 2 } - ( r - R ) ^ { 2 } )$$

Evaluate

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

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(r-R\right)^{2}.

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

To find the opposite of r^{2}-2rR+R^{2}, find the opposite of each term.

$$-r^{2}-r^{2}+2rR-R^{2}$$

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

$$-2r^{2}+2rR-R^{2}$$

Expand

$$-2r^{2}+2Rr-R^{2}$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(r-R\right)^{2}.

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

To find the opposite of r^{2}-2rR+R^{2}, find the opposite of each term.

$$-r^{2}-r^{2}+2rR-R^{2}$$

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

$$-2r^{2}+2rR-R^{2}$$