Solve (y ^ 4 - 4y ^ 3 + 6y ^ 2 - 4y + 1) - (y ^ 2 + 2y + 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

$$(y^{4}-4y^{3}+6y^{2}-4y+1)-(y^{2}+2y+1)$$

Evaluate

$y\left(y-3\right)\left(y^{2}-y+2\right)$

Solution Steps

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

$$y^{4}-4y^{3}+6y^{2}-4y+1-y^{2}-2y-1$$

Combine $6y^{2}$ and $-y^{2}$ to get $5y^{2}$.

$$y^{4}-4y^{3}+5y^{2}-4y+1-2y-1$$

Combine $-4y$ and $-2y$ to get $-6y$.

$$y^{4}-4y^{3}+5y^{2}-6y+1-1$$

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

$$y^{4}-4y^{3}+5y^{2}-6y$$

Expand

$y^{4}-4y^{3}+5y^{2}-6y$

Solution Steps

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

$$y^{4}-4y^{3}+6y^{2}-4y+1-y^{2}-2y-1$$

Combine $6y^{2}$ and $-y^{2}$ to get $5y^{2}$.

$$y^{4}-4y^{3}+5y^{2}-4y+1-2y-1$$

Combine $-4y$ and $-2y$ to get $-6y$.

$$y^{4}-4y^{3}+5y^{2}-6y+1-1$$

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

$$y^{4}-4y^{3}+5y^{2}-6y$$