Solve (2a^4-a^3-2a^2+5a-1)6(2a^2+a-3)sqrt{463}

$$( 2 a ^ { 4 } - a ^ { 3 } - 2 a ^ { 2 } + 5 a - 1 ) 6 ( 2 a ^ { 2 } + a - 3 ) \sqrt { 463 }$$

Evaluate

$$6\sqrt{463}\left(a-1\right)\left(2a+3\right)\left(2a^{4}-a^{3}-2a^{2}+5a-1\right)$$

Solution Steps

Use the distributive property to multiply 6 by 2a^{4}-a^{3}-2a^{2}+5a-1.

$$\left(12a^{4}-6a^{3}-12a^{2}+30a-6\right)\left(2a^{2}+a-3\right)\sqrt{463}$$

Use the distributive property to multiply 12a^{4}-6a^{3}-12a^{2}+30a-6 by 2a^{2}+a-3 and combine like terms.

$$\left(24a^{6}-66a^{4}+66a^{3}+54a^{2}-96a+18\right)\sqrt{463}$$

Use the distributive property to multiply 24a^{6}-66a^{4}+66a^{3}+54a^{2}-96a+18 by \sqrt{463}.

$$24a^{6}\sqrt{463}-66a^{4}\sqrt{463}+66a^{3}\sqrt{463}+54a^{2}\sqrt{463}-96a\sqrt{463}+18\sqrt{463}$$

Factor

$$6\sqrt{463}\left(a-1\right)\left(2a+3\right)\left(2a^{4}-a^{3}-2a^{2}+5a-1\right)$$