Solve 2\times(3(x)^(2)+2x-5)+(4(x)^(2)-x+3)-(2(x)^(2)+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

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

Evaluate

$8x^{2}-6$

Solution Steps

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

$$6x^{2}+4x-10+4x^{2}-x+3-\left(2x^{2}+3x-1\right)$$

Combine $6x^{2}$ and $4x^{2}$ to get $10x^{2}$.

$$10x^{2}+4x-10-x+3-\left(2x^{2}+3x-1\right)$$

Combine $4x$ and $-x$ to get $3x$.

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

Add $-10$ and $3$ to get $-7$.

$$10x^{2}+3x-7-\left(2x^{2}+3x-1\right)$$

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

$$10x^{2}+3x-7-2x^{2}-3x+1$$

Combine $10x^{2}$ and $-2x^{2}$ to get $8x^{2}$.

$$8x^{2}+3x-7-3x+1$$

Combine $3x$ and $-3x$ to get $0$.

$$8x^{2}-7+1$$

Add $-7$ and $1$ to get $-6$.

$$8x^{2}-6$$

Expand

$8x^{2}-6$

Solution Steps

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

$$6x^{2}+4x-10+4x^{2}-x+3-\left(2x^{2}+3x-1\right)$$

Combine $6x^{2}$ and $4x^{2}$ to get $10x^{2}$.

$$10x^{2}+4x-10-x+3-\left(2x^{2}+3x-1\right)$$

Combine $4x$ and $-x$ to get $3x$.

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

Add $-10$ and $3$ to get $-7$.

$$10x^{2}+3x-7-\left(2x^{2}+3x-1\right)$$

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

$$10x^{2}+3x-7-2x^{2}-3x+1$$

Combine $10x^{2}$ and $-2x^{2}$ to get $8x^{2}$.

$$8x^{2}+3x-7-3x+1$$

Combine $3x$ and $-3x$ to get $0$.

$$8x^{2}-7+1$$

Add $-7$ and $1$ to get $-6$.

$$8x^{2}-6$$