Solve (x ^ 2 - x + 1) ^ 2 - (x ^ 2 + x + 1) ^ 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

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

Evaluate

$-4x\left(x^{2}+1\right)$

Solution Steps

Square $x^{2}-x+1$.

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

Square $x^{2}+x+1$.

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

To find the opposite of $x^{4}+2x^{3}+3x^{2}+2x+1$, find the opposite of each term.

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

Combine $x^{4}$ and $-x^{4}$ to get $0$.

$$-2x^{3}+3x^{2}-2x+1-2x^{3}-3x^{2}-2x-1$$

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

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

Combine $3x^{2}$ and $-3x^{2}$ to get $0$.

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

Combine $-2x$ and $-2x$ to get $-4x$.

$$-4x^{3}-4x+1-1$$

Subtract $1$ from $1$ to get $0$.

$$-4x^{3}-4x$$

Expand

$-4x^{3}-4x$

Solution Steps

Square $x^{2}-x+1$.

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

Square $x^{2}+x+1$.

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

To find the opposite of $x^{4}+2x^{3}+3x^{2}+2x+1$, find the opposite of each term.

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

Combine $x^{4}$ and $-x^{4}$ to get $0$.

$$-2x^{3}+3x^{2}-2x+1-2x^{3}-3x^{2}-2x-1$$

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

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

Combine $3x^{2}$ and $-3x^{2}$ to get $0$.

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

Combine $-2x$ and $-2x$ to get $-4x$.

$$-4x^{3}-4x+1-1$$

Subtract $1$ from $1$ to get $0$.

$$-4x^{3}-4x$$