Solve (4R+7R_{2})+(5R_{1}-3R_{2})+(2R_{2}-R_{1})

$$( 4 R + 7 R _ { 2 } ) + ( 5 R _ { 1 } - 3 R _ { 2 } ) + ( 2 R _ { 2 } - R _ { 1 } )$$

Evaluate

$$4R+4R_{1}+6R_{2}$$

Solution Steps

Combine 7R_{2} and -3R_{2} to get 4R_{2}.

$$4R+4R_{2}+5R_{1}+2R_{2}-R_{1}$$

Combine 4R_{2} and 2R_{2} to get 6R_{2}.

$$4R+6R_{2}+5R_{1}-R_{1}$$

Combine 5R_{1} and -R_{1} to get 4R_{1}.

$$4R+6R_{2}+4R_{1}$$

Factor

$$2\left(2R+2R_{1}+3R_{2}\right)$$

Solution Steps

Multiply and combine like terms.

$$4R+4R_{1}+6R_{2}$$

Factor out 2.

$$2\left(2R+2R_{1}+3R_{2}\right)$$