Solve 4a * (a - 1) ^ 2 - (1 - a) | 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

$$4a(a-1)^{2}-(1-a)$$

Evaluate

$\left(a-1\right)\left(2a-1\right)^{2}$

Solution Steps

Use binomial theorem $\left(p-q\right)^{2}=p^{2}-2pq+q^{2}$ to expand $\left(a-1\right)^{2}$.

$$4a\left(a^{2}-2a+1\right)-\left(1-a\right)$$

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

$$4a^{3}-8a^{2}+4a-\left(1-a\right)$$

To find the opposite of $1-a$, find the opposite of each term.

$$4a^{3}-8a^{2}+4a-1+a$$

Combine $4a$ and $a$ to get $5a$.

$$4a^{3}-8a^{2}+5a-1$$

Expand

$4a^{3}-8a^{2}+5a-1$

Solution Steps

Use binomial theorem $\left(p-q\right)^{2}=p^{2}-2pq+q^{2}$ to expand $\left(a-1\right)^{2}$.

$$4a\left(a^{2}-2a+1\right)-\left(1-a\right)$$

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

$$4a^{3}-8a^{2}+4a-\left(1-a\right)$$

To find the opposite of $1-a$, find the opposite of each term.

$$4a^{3}-8a^{2}+4a-1+a$$

Combine $4a$ and $a$ to get $5a$.

$$4a^{3}-8a^{2}+5a-1$$