Solve (2(x)^(3)-(x)^(2)+6x-1)((x)^(2)-8x+2)-3x((x)^(3)-(x)^(2)+6x-7) | 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

$$(2 { x }^{ 3 } - { x }^{ 2 } +6x-1)( { x }^{ 2 } -8x+2)-3x( { x }^{ 3 } - { x }^{ 2 } +6x-7)$$

Evaluate

$2x^{5}-20x^{4}+21x^{3}-69x^{2}+41x-2$

Solution Steps

Use the distributive property to multiply $2x^{3}-x^{2}+6x-1$ by $x^{2}-8x+2$ and combine like terms.

$$2x^{5}-17x^{4}+18x^{3}-51x^{2}+20x-2-3x\left(x^{3}-x^{2}+6x-7\right)$$

Use the distributive property to multiply $-3x$ by $x^{3}-x^{2}+6x-7$.

$$2x^{5}-17x^{4}+18x^{3}-51x^{2}+20x-2-3x^{4}+3x^{3}-18x^{2}+21x$$

Combine $-17x^{4}$ and $-3x^{4}$ to get $-20x^{4}$.

$$2x^{5}-20x^{4}+18x^{3}-51x^{2}+20x-2+3x^{3}-18x^{2}+21x$$

Combine $18x^{3}$ and $3x^{3}$ to get $21x^{3}$.

$$2x^{5}-20x^{4}+21x^{3}-51x^{2}+20x-2-18x^{2}+21x$$

Combine $-51x^{2}$ and $-18x^{2}$ to get $-69x^{2}$.

$$2x^{5}-20x^{4}+21x^{3}-69x^{2}+20x-2+21x$$

Combine $20x$ and $21x$ to get $41x$.

$$2x^{5}-20x^{4}+21x^{3}-69x^{2}+41x-2$$

Expand

$2x^{5}-20x^{4}+21x^{3}-69x^{2}+41x-2$

Solution Steps

Use the distributive property to multiply $2x^{3}-x^{2}+6x-1$ by $x^{2}-8x+2$ and combine like terms.

$$2x^{5}-17x^{4}+18x^{3}-51x^{2}+20x-2-3x\left(x^{3}-x^{2}+6x-7\right)$$

Use the distributive property to multiply $-3x$ by $x^{3}-x^{2}+6x-7$.

$$2x^{5}-17x^{4}+18x^{3}-51x^{2}+20x-2-3x^{4}+3x^{3}-18x^{2}+21x$$

Combine $-17x^{4}$ and $-3x^{4}$ to get $-20x^{4}$.

$$2x^{5}-20x^{4}+18x^{3}-51x^{2}+20x-2+3x^{3}-18x^{2}+21x$$

Combine $18x^{3}$ and $3x^{3}$ to get $21x^{3}$.

$$2x^{5}-20x^{4}+21x^{3}-51x^{2}+20x-2-18x^{2}+21x$$

Combine $-51x^{2}$ and $-18x^{2}$ to get $-69x^{2}$.

$$2x^{5}-20x^{4}+21x^{3}-69x^{2}+20x-2+21x$$

Combine $20x$ and $21x$ to get $41x$.

$$2x^{5}-20x^{4}+21x^{3}-69x^{2}+41x-2$$