Solve 3\times(4(x)^(2)-3x+1)+2-((x)^(2)-x+5)-(3(x)^(2)-x-4) | 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

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

Evaluate

$8x^{2}-7x+4$

Solution Steps

Use the distributive property to multiply $3$ by $4x^{2}-3x+1$.

$$12x^{2}-9x+3+2-\left(x^{2}-x+5\right)-\left(3x^{2}-x-4\right)$$

Add $3$ and $2$ to get $5$.

$$12x^{2}-9x+5-\left(x^{2}-x+5\right)-\left(3x^{2}-x-4\right)$$

To find the opposite of $x^{2}-x+5$, find the opposite of each term.

$$12x^{2}-9x+5-x^{2}+x-5-\left(3x^{2}-x-4\right)$$

Combine $12x^{2}$ and $-x^{2}$ to get $11x^{2}$.

$$11x^{2}-9x+5+x-5-\left(3x^{2}-x-4\right)$$

Combine $-9x$ and $x$ to get $-8x$.

$$11x^{2}-8x+5-5-\left(3x^{2}-x-4\right)$$

Subtract $5$ from $5$ to get $0$.

$$11x^{2}-8x-\left(3x^{2}-x-4\right)$$

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

$$11x^{2}-8x-3x^{2}+x+4$$

Combine $11x^{2}$ and $-3x^{2}$ to get $8x^{2}$.

$$8x^{2}-8x+x+4$$

Combine $-8x$ and $x$ to get $-7x$.

$$8x^{2}-7x+4$$

Expand

$8x^{2}-7x+4$

Solution Steps

Use the distributive property to multiply $3$ by $4x^{2}-3x+1$.

$$12x^{2}-9x+3+2-\left(x^{2}-x+5\right)-\left(3x^{2}-x-4\right)$$

Add $3$ and $2$ to get $5$.

$$12x^{2}-9x+5-\left(x^{2}-x+5\right)-\left(3x^{2}-x-4\right)$$

To find the opposite of $x^{2}-x+5$, find the opposite of each term.

$$12x^{2}-9x+5-x^{2}+x-5-\left(3x^{2}-x-4\right)$$

Combine $12x^{2}$ and $-x^{2}$ to get $11x^{2}$.

$$11x^{2}-9x+5+x-5-\left(3x^{2}-x-4\right)$$

Combine $-9x$ and $x$ to get $-8x$.

$$11x^{2}-8x+5-5-\left(3x^{2}-x-4\right)$$

Subtract $5$ from $5$ to get $0$.

$$11x^{2}-8x-\left(3x^{2}-x-4\right)$$

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

$$11x^{2}-8x-3x^{2}+x+4$$

Combine $11x^{2}$ and $-3x^{2}$ to get $8x^{2}$.

$$8x^{2}-8x+x+4$$

Combine $-8x$ and $x$ to get $-7x$.

$$8x^{2}-7x+4$$