Solve (a+b)^(3)+3ab(1-a-b)-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

$${ \left(a+b \right) }^{ 3 } +3ab(1-a-b)-1$$

Evaluate

$a^{3}+3ab+b^{3}-1$

Solution Steps

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

$$a^{3}+3a^{2}b+3ab^{2}+b^{3}+3ab\left(1-a-b\right)-1$$

Use the distributive property to multiply $3ab$ by $1-a-b$.

$$a^{3}+3a^{2}b+3ab^{2}+b^{3}+3ab-3a^{2}b-3ab^{2}-1$$

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

$$a^{3}+3ab^{2}+b^{3}+3ab-3ab^{2}-1$$

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

$$a^{3}+b^{3}+3ab-1$$

Expand

$a^{3}+3ab+b^{3}-1$

Solution Steps

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

$$a^{3}+3a^{2}b+3ab^{2}+b^{3}+3ab\left(1-a-b\right)-1$$

Use the distributive property to multiply $3ab$ by $1-a-b$.

$$a^{3}+3a^{2}b+3ab^{2}+b^{3}+3ab-3a^{2}b-3ab^{2}-1$$

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

$$a^{3}+3ab^{2}+b^{3}+3ab-3ab^{2}-1$$

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

$$a^{3}+b^{3}+3ab-1$$