Solve (6-9(x)^(2)+5x-2)-((x)^(2)-8x+1)-(2(x)^(2)+4x-6) | 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

$$(6-9 { x }^{ 2 } +5x-2)-( { x }^{ 2 } -8x+1)-(2 { x }^{ 2 } +4x-6)$$

Evaluate

$9+9x-12x^{2}$

Solution Steps

Subtract $2$ from $6$ to get $4$.

$$4-9x^{2}+5x-\left(x^{2}-8x+1\right)-\left(2x^{2}+4x-6\right)$$

To find the opposite of $x^{2}-8x+1$, find the opposite of each term.

$$4-9x^{2}+5x-x^{2}+8x-1-\left(2x^{2}+4x-6\right)$$

Combine $-9x^{2}$ and $-x^{2}$ to get $-10x^{2}$.

$$4-10x^{2}+5x+8x-1-\left(2x^{2}+4x-6\right)$$

Combine $5x$ and $8x$ to get $13x$.

$$4-10x^{2}+13x-1-\left(2x^{2}+4x-6\right)$$

Subtract $1$ from $4$ to get $3$.

$$3-10x^{2}+13x-\left(2x^{2}+4x-6\right)$$

To find the opposite of $2x^{2}+4x-6$, find the opposite of each term.

$$3-10x^{2}+13x-2x^{2}-4x+6$$

Combine $-10x^{2}$ and $-2x^{2}$ to get $-12x^{2}$.

$$3-12x^{2}+13x-4x+6$$

Combine $13x$ and $-4x$ to get $9x$.

$$3-12x^{2}+9x+6$$

Add $3$ and $6$ to get $9$.

$$9-12x^{2}+9x$$

Expand

$9+9x-12x^{2}$

Solution Steps

Subtract $2$ from $6$ to get $4$.

$$4-9x^{2}+5x-\left(x^{2}-8x+1\right)-\left(2x^{2}+4x-6\right)$$

To find the opposite of $x^{2}-8x+1$, find the opposite of each term.

$$4-9x^{2}+5x-x^{2}+8x-1-\left(2x^{2}+4x-6\right)$$

Combine $-9x^{2}$ and $-x^{2}$ to get $-10x^{2}$.

$$4-10x^{2}+5x+8x-1-\left(2x^{2}+4x-6\right)$$

Combine $5x$ and $8x$ to get $13x$.

$$4-10x^{2}+13x-1-\left(2x^{2}+4x-6\right)$$

Subtract $1$ from $4$ to get $3$.

$$3-10x^{2}+13x-\left(2x^{2}+4x-6\right)$$

To find the opposite of $2x^{2}+4x-6$, find the opposite of each term.

$$3-10x^{2}+13x-2x^{2}-4x+6$$

Combine $-10x^{2}$ and $-2x^{2}$ to get $-12x^{2}$.

$$3-12x^{2}+13x-4x+6$$

Combine $13x$ and $-4x$ to get $9x$.

$$3-12x^{2}+9x+6$$

Add $3$ and $6$ to get $9$.

$$9-12x^{2}+9x$$