Solve (2(x)^(4)+3x-(x)^(3)-9)((x)^(2)+3x+8)-3x((x)^(4)-(x)^(3)+3(x)^(2)-4) | Equatix - Math Solver

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Example

3(r+2s)=2t-4

a⋅(b-2)=3b

3(r+2s)=2t-4

a⋅(b-2)=3b

Question

$$(2 { x }^{ 4 } +3x- { x }^{ 3 } -9)( { x }^{ 2 } +3x+8)-3x( { x }^{ 4 } - { x }^{ 3 } +3 { x }^{ 2 } -4)$$

Evaluate

$2x^{6}+2x^{5}+16x^{4}-14x^{3}+9x-72$

Solution Steps

Use the distributive property to multiply $2x^{4}+3x-x^{3}-9$ by $x^{2}+3x+8$ and combine like terms.

$$2x^{6}+5x^{5}+13x^{4}-5x^{3}-3x-72-3x\left(x^{4}-x^{3}+3x^{2}-4\right)$$

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

$$2x^{6}+5x^{5}+13x^{4}-5x^{3}-3x-72-3x^{5}+3x^{4}-9x^{3}+12x$$

Combine $5x^{5}$ and $-3x^{5}$ to get $2x^{5}$.

$$2x^{6}+2x^{5}+13x^{4}-5x^{3}-3x-72+3x^{4}-9x^{3}+12x$$

Combine $13x^{4}$ and $3x^{4}$ to get $16x^{4}$.

$$2x^{6}+2x^{5}+16x^{4}-5x^{3}-3x-72-9x^{3}+12x$$

Combine $-5x^{3}$ and $-9x^{3}$ to get $-14x^{3}$.

$$2x^{6}+2x^{5}+16x^{4}-14x^{3}-3x-72+12x$$

Combine $-3x$ and $12x$ to get $9x$.

$$2x^{6}+2x^{5}+16x^{4}-14x^{3}+9x-72$$

Expand

$2x^{6}+2x^{5}+16x^{4}-14x^{3}+9x-72$

Solution Steps

Use the distributive property to multiply $2x^{4}+3x-x^{3}-9$ by $x^{2}+3x+8$ and combine like terms.

$$2x^{6}+5x^{5}+13x^{4}-5x^{3}-3x-72-3x\left(x^{4}-x^{3}+3x^{2}-4\right)$$

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

$$2x^{6}+5x^{5}+13x^{4}-5x^{3}-3x-72-3x^{5}+3x^{4}-9x^{3}+12x$$

Combine $5x^{5}$ and $-3x^{5}$ to get $2x^{5}$.

$$2x^{6}+2x^{5}+13x^{4}-5x^{3}-3x-72+3x^{4}-9x^{3}+12x$$

Combine $13x^{4}$ and $3x^{4}$ to get $16x^{4}$.

$$2x^{6}+2x^{5}+16x^{4}-5x^{3}-3x-72-9x^{3}+12x$$

Combine $-5x^{3}$ and $-9x^{3}$ to get $-14x^{3}$.

$$2x^{6}+2x^{5}+16x^{4}-14x^{3}-3x-72+12x$$

Combine $-3x$ and $12x$ to get $9x$.

$$2x^{6}+2x^{5}+16x^{4}-14x^{3}+9x-72$$