Solve (2(x)^(2)-3x+1)((1)/(2)x+(3)/(2))-x(x-(1)/(2)(x+3)) | 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

$$(2 { x }^{ 2 } -3x+1)( \frac{ 1 }{ 2 } x+ \frac{ 3 }{ 2 } )-x(x- \frac{ 1 }{ 2 } (x+3))$$

Evaluate

$x^{3}+x^{2}-\frac{5x}{2}+\frac{3}{2}$

Solution Steps

Use the distributive property to multiply $2x^{2}-3x+1$ by $\frac{1}{2}x+\frac{3}{2}$ and combine like terms.

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

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

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

Combine $x$ and $-\frac{1}{2}x$ to get $\frac{1}{2}x$.

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

Use the distributive property to multiply $x$ by $\frac{1}{2}x-\frac{3}{2}$.

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

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

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

Combine $\frac{3}{2}x^{2}$ and $-\frac{1}{2}x^{2}$ to get $x^{2}$.

$$x^{3}+x^{2}-4x+\frac{3}{2}+\frac{3}{2}x$$

Combine $-4x$ and $\frac{3}{2}x$ to get $-\frac{5}{2}x$.

$$x^{3}+x^{2}-\frac{5}{2}x+\frac{3}{2}$$

Expand

$x^{3}+x^{2}-\frac{5x}{2}+\frac{3}{2}$

Solution Steps

Use the distributive property to multiply $2x^{2}-3x+1$ by $\frac{1}{2}x+\frac{3}{2}$ and combine like terms.

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

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

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

Combine $x$ and $-\frac{1}{2}x$ to get $\frac{1}{2}x$.

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

Use the distributive property to multiply $x$ by $\frac{1}{2}x-\frac{3}{2}$.

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

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

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

Combine $\frac{3}{2}x^{2}$ and $-\frac{1}{2}x^{2}$ to get $x^{2}$.

$$x^{3}+x^{2}-4x+\frac{3}{2}+\frac{3}{2}x$$

Combine $-4x$ and $\frac{3}{2}x$ to get $-\frac{5}{2}x$.

$$x^{3}+x^{2}-\frac{5}{2}x+\frac{3}{2}$$