Solve (5(x)^(2)-2)((x)^(2)+3x-1)+(x-1)((x)^(3)+3x-1) | 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

$$(5 { x }^{ 2 } -2)( { x }^{ 2 } +3x-1)+(x-1)( { x }^{ 3 } +3x-1)$$

Evaluate

$6x^{4}+14x^{3}-4x^{2}-10x+3$

Solution Steps

Use the distributive property to multiply $5x^{2}-2$ by $x^{2}+3x-1$ and combine like terms.

$$5x^{4}+15x^{3}-7x^{2}-6x+2+\left(x-1\right)\left(x^{3}+3x-1\right)$$

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

$$5x^{4}+15x^{3}-7x^{2}-6x+2+x^{4}+3x^{2}-4x-x^{3}+1$$

Combine $5x^{4}$ and $x^{4}$ to get $6x^{4}$.

$$6x^{4}+15x^{3}-7x^{2}-6x+2+3x^{2}-4x-x^{3}+1$$

Combine $-7x^{2}$ and $3x^{2}$ to get $-4x^{2}$.

$$6x^{4}+15x^{3}-4x^{2}-6x+2-4x-x^{3}+1$$

Combine $-6x$ and $-4x$ to get $-10x$.

$$6x^{4}+15x^{3}-4x^{2}-10x+2-x^{3}+1$$

Combine $15x^{3}$ and $-x^{3}$ to get $14x^{3}$.

$$6x^{4}+14x^{3}-4x^{2}-10x+2+1$$

Add $2$ and $1$ to get $3$.

$$6x^{4}+14x^{3}-4x^{2}-10x+3$$

Expand

$6x^{4}+14x^{3}-4x^{2}-10x+3$

Solution Steps

Use the distributive property to multiply $5x^{2}-2$ by $x^{2}+3x-1$ and combine like terms.

$$5x^{4}+15x^{3}-7x^{2}-6x+2+\left(x-1\right)\left(x^{3}+3x-1\right)$$

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

$$5x^{4}+15x^{3}-7x^{2}-6x+2+x^{4}+3x^{2}-4x-x^{3}+1$$

Combine $5x^{4}$ and $x^{4}$ to get $6x^{4}$.

$$6x^{4}+15x^{3}-7x^{2}-6x+2+3x^{2}-4x-x^{3}+1$$

Combine $-7x^{2}$ and $3x^{2}$ to get $-4x^{2}$.

$$6x^{4}+15x^{3}-4x^{2}-6x+2-4x-x^{3}+1$$

Combine $-6x$ and $-4x$ to get $-10x$.

$$6x^{4}+15x^{3}-4x^{2}-10x+2-x^{3}+1$$

Combine $15x^{3}$ and $-x^{3}$ to get $14x^{3}$.

$$6x^{4}+14x^{3}-4x^{2}-10x+2+1$$

Add $2$ and $1$ to get $3$.

$$6x^{4}+14x^{3}-4x^{2}-10x+3$$