Solve (8b^{2}-4b+3b^{4}+2b^3)+(4b^2-7b^4-b^3)

$$( 8 b ^ { 2 } - 4 b + 3 b ^ { 4 } + 2 b ^ { 3 } ) + ( 4 b ^ { 2 } - 7 b ^ { 4 } - b ^ { 3 } )$$

Evaluate

$$b\left(-4b^{3}+b^{2}+12b-4\right)$$

Solution Steps

Combine 8b^{2} and 4b^{2} to get 12b^{2}.

$$12b^{2}-4b+3b^{4}+2b^{3}-7b^{4}-b^{3}$$

Combine 3b^{4} and -7b^{4} to get -4b^{4}.

$$12b^{2}-4b-4b^{4}+2b^{3}-b^{3}$$

Combine 2b^{3} and -b^{3} to get b^{3}.

$$12b^{2}-4b-4b^{4}+b^{3}$$

Factor

$$b\left(-4b^{3}+b^{2}+12b-4\right)$$

Solution Steps

Factor out b. Polynomial -4b^{3}+b^{2}+12b-4 is not factored since it does not have any rational roots.

$$b\left(8b-4+3b^{3}+2b^{2}+4b-7b^{3}-b^{2}\right)$$