Solve =4x_{1}x_{1}+5x_{1}x_{2}+5x_{2}x_{1}+100x_{2}x_{2}

$$= 4 x _ { 1 } x _ { 1 } + 5 x _ { 1 } x _ { 2 } + 5 x _ { 2 } x _ { 1 } + 100 x _ { 2 } x _ { 2 }$$

Evaluate

$$4x_{1}^{2}+10x_{1}x_{2}+100x_{2}^{2}$$

Solution Steps

Multiply x_{1} and x_{1} to get x_{1}^{2}.

$$4x_{1}^{2}+5x_{1}x_{2}+5x_{2}x_{1}+100x_{2}x_{2}$$

Multiply x_{2} and x_{2} to get x_{2}^{2}.

$$4x_{1}^{2}+5x_{1}x_{2}+5x_{2}x_{1}+100x_{2}^{2}$$

Combine 5x_{1}x_{2} and 5x_{2}x_{1} to get 10x_{1}x_{2}.

$$4x_{1}^{2}+10x_{1}x_{2}+100x_{2}^{2}$$

Factor

$$2\left(2x_{1}^{2}+5x_{1}x_{2}+50x_{2}^{2}\right)$$

Solution Steps

Multiply and combine like terms.

$$4x_{1}^{2}+10x_{1}x_{2}+100x_{2}^{2}$$

Factor out 2.

$$2\left(2x_{1}^{2}+5x_{1}x_{2}+50x_{2}^{2}\right)$$