Solve 5\times(2(x)^(3)-4x+6)-((x)^(3)+2(x)^(2)-3x+1)+5(x)^(3)-2(x)^(2)= | 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

$$5 \times (2 { x }^{ 3 } -4x+6)-( { x }^{ 3 } +2 { x }^{ 2 } -3x+1)+5 { x }^{ 3 } -2 { x }^{ 2 } =$$

Evaluate

$14x^{3}-4x^{2}-17x+29$

Solution Steps

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

$$10x^{3}-20x+30-\left(x^{3}+2x^{2}-3x+1\right)+5x^{3}-2x^{2}$$

To find the opposite of $x^{3}+2x^{2}-3x+1$, find the opposite of each term.

$$10x^{3}-20x+30-x^{3}-2x^{2}+3x-1+5x^{3}-2x^{2}$$

Combine $10x^{3}$ and $-x^{3}$ to get $9x^{3}$.

$$9x^{3}-20x+30-2x^{2}+3x-1+5x^{3}-2x^{2}$$

Combine $-20x$ and $3x$ to get $-17x$.

$$9x^{3}-17x+30-2x^{2}-1+5x^{3}-2x^{2}$$

Subtract $1$ from $30$ to get $29$.

$$9x^{3}-17x+29-2x^{2}+5x^{3}-2x^{2}$$

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

$$14x^{3}-17x+29-2x^{2}-2x^{2}$$

Combine $-2x^{2}$ and $-2x^{2}$ to get $-4x^{2}$.

$$14x^{3}-17x+29-4x^{2}$$

Expand

$14x^{3}-4x^{2}-17x+29$

Solution Steps

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

$$10x^{3}-20x+30-\left(x^{3}+2x^{2}-3x+1\right)+5x^{3}-2x^{2}$$

To find the opposite of $x^{3}+2x^{2}-3x+1$, find the opposite of each term.

$$10x^{3}-20x+30-x^{3}-2x^{2}+3x-1+5x^{3}-2x^{2}$$

Combine $10x^{3}$ and $-x^{3}$ to get $9x^{3}$.

$$9x^{3}-20x+30-2x^{2}+3x-1+5x^{3}-2x^{2}$$

Combine $-20x$ and $3x$ to get $-17x$.

$$9x^{3}-17x+30-2x^{2}-1+5x^{3}-2x^{2}$$

Subtract $1$ from $30$ to get $29$.

$$9x^{3}-17x+29-2x^{2}+5x^{3}-2x^{2}$$

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

$$14x^{3}-17x+29-2x^{2}-2x^{2}$$

Combine $-2x^{2}$ and $-2x^{2}$ to get $-4x^{2}$.

$$14x^{3}-17x+29-4x^{2}$$