Solve (r-2s)(r+2s)+r(2r-s)

$$( r - 2 s ) ( r + 2 s ) + r ( 2 r - s )$$

Evaluate

$$\left(3r-4s\right)\left(r+s\right)$$

Solution Steps

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

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

Expand \left(2s\right)^{2}.

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

Calculate 2 to the power of 2 and get 4.

$$r^{2}-4s^{2}+r\left(2r-s\right)$$

Use the distributive property to multiply r by 2r-s.

$$r^{2}-4s^{2}+2r^{2}-rs$$

Combine r^{2} and 2r^{2} to get 3r^{2}.

$$3r^{2}-4s^{2}-rs$$

Expand

$$3r^{2}-rs-4s^{2}$$

Solution Steps

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

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

Expand \left(2s\right)^{2}.

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

Calculate 2 to the power of 2 and get 4.

$$r^{2}-4s^{2}+r\left(2r-s\right)$$

Use the distributive property to multiply r by 2r-s.

$$r^{2}-4s^{2}+2r^{2}-rs$$

Combine r^{2} and 2r^{2} to get 3r^{2}.

$$3r^{2}-4s^{2}-rs$$