Solve (4x^3-5x+7)(12x^3-6x^2)+(3x^4-2{x}^3+2)(12{x}^2-5)

$$(4 { x }^{ 3 } -5x+7)(12 { x }^{ 3 } -6 { x }^{ 2 } )+(3 { x }^{ 4 } -2 { x }^{ 3 } +2)(12 { x }^{ 2 } -5)$$

Evaluate

$$84x^{6}-48x^{5}-75x^{4}+124x^{3}-18x^{2}-10$$

Solution Steps

Use the distributive property to multiply 4x^{3}-5x+7 by 12x^{3}-6x^{2} and combine like terms.

$$48x^{6}-24x^{5}-60x^{4}+114x^{3}-42x^{2}+\left(3x^{4}-2x^{3}+2\right)\left(12x^{2}-5\right)$$

Use the distributive property to multiply 3x^{4}-2x^{3}+2 by 12x^{2}-5.

$$48x^{6}-24x^{5}-60x^{4}+114x^{3}-42x^{2}+36x^{6}-15x^{4}-24x^{5}+10x^{3}+24x^{2}-10$$

Combine 48x^{6} and 36x^{6} to get 84x^{6}.

$$84x^{6}-24x^{5}-60x^{4}+114x^{3}-42x^{2}-15x^{4}-24x^{5}+10x^{3}+24x^{2}-10$$

Combine -60x^{4} and -15x^{4} to get -75x^{4}.

$$84x^{6}-24x^{5}-75x^{4}+114x^{3}-42x^{2}-24x^{5}+10x^{3}+24x^{2}-10$$

Combine -24x^{5} and -24x^{5} to get -48x^{5}.

$$84x^{6}-48x^{5}-75x^{4}+114x^{3}-42x^{2}+10x^{3}+24x^{2}-10$$

Combine 114x^{3} and 10x^{3} to get 124x^{3}.

$$84x^{6}-48x^{5}-75x^{4}+124x^{3}-42x^{2}+24x^{2}-10$$

Combine -42x^{2} and 24x^{2} to get -18x^{2}.

$$84x^{6}-48x^{5}-75x^{4}+124x^{3}-18x^{2}-10$$

Expand

$$84x^{6}-48x^{5}-75x^{4}+124x^{3}-18x^{2}-10$$

Solution Steps

Use the distributive property to multiply 4x^{3}-5x+7 by 12x^{3}-6x^{2} and combine like terms.

$$48x^{6}-24x^{5}-60x^{4}+114x^{3}-42x^{2}+\left(3x^{4}-2x^{3}+2\right)\left(12x^{2}-5\right)$$

Use the distributive property to multiply 3x^{4}-2x^{3}+2 by 12x^{2}-5.

$$48x^{6}-24x^{5}-60x^{4}+114x^{3}-42x^{2}+36x^{6}-15x^{4}-24x^{5}+10x^{3}+24x^{2}-10$$

Combine 48x^{6} and 36x^{6} to get 84x^{6}.

$$84x^{6}-24x^{5}-60x^{4}+114x^{3}-42x^{2}-15x^{4}-24x^{5}+10x^{3}+24x^{2}-10$$

Combine -60x^{4} and -15x^{4} to get -75x^{4}.

$$84x^{6}-24x^{5}-75x^{4}+114x^{3}-42x^{2}-24x^{5}+10x^{3}+24x^{2}-10$$

Combine -24x^{5} and -24x^{5} to get -48x^{5}.

$$84x^{6}-48x^{5}-75x^{4}+114x^{3}-42x^{2}+10x^{3}+24x^{2}-10$$

Combine 114x^{3} and 10x^{3} to get 124x^{3}.

$$84x^{6}-48x^{5}-75x^{4}+124x^{3}-42x^{2}+24x^{2}-10$$

Combine -42x^{2} and 24x^{2} to get -18x^{2}.

$$84x^{6}-48x^{5}-75x^{4}+124x^{3}-18x^{2}-10$$