Solve (a + b) ^ 3 = a ^ 3 + b ^ 3 + 3a ^ 2 * b + 3a * b ^ 2 * b | 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

$$(a+b)^{3}=a^{3}+b^{3}+3a^{2}b+3ab^{2}b$$

Solve for a (complex solution)

$\left\{\begin{matrix}\\a=0\text{, }&\text{unconditionally}\\a\in \mathrm{C}\text{, }&b=0\text{ or }b=1\end{matrix}\right.$

Steps for Solving Linear Equation

To multiply powers of the same base, add their exponents. Add $2$ and $1$ to get $3$.

$$\left(a+b\right)^{3}=a^{3}+b^{3}+3a^{2}b+3ab^{3}$$

Use binomial theorem $\left(p+q\right)^{3}=p^{3}+3p^{2}q+3pq^{2}+q^{3}$ to expand $\left(a+b\right)^{3}$.

$$a^{3}+3a^{2}b+3ab^{2}+b^{3}=a^{3}+b^{3}+3a^{2}b+3ab^{3}$$

Subtract $a^{3}$ from both sides.

$$a^{3}+3a^{2}b+3ab^{2}+b^{3}-a^{3}=b^{3}+3a^{2}b+3ab^{3}$$

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

$$3a^{2}b+3ab^{2}+b^{3}=b^{3}+3a^{2}b+3ab^{3}$$

Subtract $3a^{2}b$ from both sides.

$$3a^{2}b+3ab^{2}+b^{3}-3a^{2}b=b^{3}+3ab^{3}$$

Combine $3a^{2}b$ and $-3a^{2}b$ to get $0$.

$$3ab^{2}+b^{3}=b^{3}+3ab^{3}$$

Subtract $3ab^{3}$ from both sides.

$$3ab^{2}+b^{3}-3ab^{3}=b^{3}$$

Subtract $b^{3}$ from both sides.

$$3ab^{2}-3ab^{3}=b^{3}-b^{3}$$

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

$$3ab^{2}-3ab^{3}=0$$

Combine all terms containing $a$.

$$\left(3b^{2}-3b^{3}\right)a=0$$

Divide $0$ by $3b^{2}-3b^{3}$.

$$a=0$$

Solve for a

$\left\{\begin{matrix}\\a=0\text{, }&\text{unconditionally}\\a\in \mathrm{R}\text{, }&b=0\text{ or }b=1\end{matrix}\right.$

Steps for Solving Linear Equation

To multiply powers of the same base, add their exponents. Add $2$ and $1$ to get $3$.

$$\left(a+b\right)^{3}=a^{3}+b^{3}+3a^{2}b+3ab^{3}$$

Use binomial theorem $\left(p+q\right)^{3}=p^{3}+3p^{2}q+3pq^{2}+q^{3}$ to expand $\left(a+b\right)^{3}$.

$$a^{3}+3a^{2}b+3ab^{2}+b^{3}=a^{3}+b^{3}+3a^{2}b+3ab^{3}$$

Subtract $a^{3}$ from both sides.

$$a^{3}+3a^{2}b+3ab^{2}+b^{3}-a^{3}=b^{3}+3a^{2}b+3ab^{3}$$

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

$$3a^{2}b+3ab^{2}+b^{3}=b^{3}+3a^{2}b+3ab^{3}$$

Subtract $3a^{2}b$ from both sides.

$$3a^{2}b+3ab^{2}+b^{3}-3a^{2}b=b^{3}+3ab^{3}$$

Combine $3a^{2}b$ and $-3a^{2}b$ to get $0$.

$$3ab^{2}+b^{3}=b^{3}+3ab^{3}$$

Subtract $3ab^{3}$ from both sides.

$$3ab^{2}+b^{3}-3ab^{3}=b^{3}$$

Subtract $b^{3}$ from both sides.

$$3ab^{2}-3ab^{3}=b^{3}-b^{3}$$

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

$$3ab^{2}-3ab^{3}=0$$

Combine all terms containing $a$.

$$\left(3b^{2}-3b^{3}\right)a=0$$

Divide $0$ by $3b^{2}-3b^{3}$.

$$a=0$$

Solve for b (complex solution)

$\left\{\begin{matrix}\\b=0\text{; }b=1\text{, }&\text{unconditionally}\\b\in \mathrm{C}\text{, }&a=0\end{matrix}\right.$

Solve for b

$\left\{\begin{matrix}\\b=0\text{; }b=1\text{, }&\text{unconditionally}\\b\in \mathrm{R}\text{, }&a=0\end{matrix}\right.$