Solve B = (x - 1) ^ 2 * (x + 2) - x * (x + 1) ^ 2 | 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

$$B=(x-1)^{2}(x+2)-x(x+1)^{2}$$

Solve for B

$B=2-4x-2x^{2}$

Solution Steps

Use binomial theorem $\left(a-b\right)^{2}=a^{2}-2ab+b^{2}$ to expand $\left(x-1\right)^{2}$.

$$B=\left(x^{2}-2x+1\right)\left(x+2\right)-x\left(x+1\right)^{2}$$

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

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

Use binomial theorem $\left(a+b\right)^{2}=a^{2}+2ab+b^{2}$ to expand $\left(x+1\right)^{2}$.

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

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

$$B=x^{3}-3x+2-\left(x^{3}+2x^{2}+x\right)$$

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

$$B=x^{3}-3x+2-x^{3}-2x^{2}-x$$

Combine $x^{3}$ and $-x^{3}$ to get $0$.

$$B=-3x+2-2x^{2}-x$$

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

$$B=-4x+2-2x^{2}$$

Solve for x (complex solution)

$x=\frac{\sqrt{8-2B}}{2}-1$
$x=-\frac{\sqrt{8-2B}}{2}-1$

Solve for x

$x=\frac{\sqrt{8-2B}}{2}-1$
$x=-\frac{\sqrt{8-2B}}{2}-1\text{, }B\leq 4$