Solve (a-1)(2a+1)-(2a-1)(a+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

$$(a-1)(2a+1)-(2a-1)(a+1$$

Evaluate

$-2a$

Solution Steps

Apply the distributive property by multiplying each term of $a-1$ by each term of $2a+1$.

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

Combine $a$ and $-2a$ to get $-a$.

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

Apply the distributive property by multiplying each term of $2a-1$ by each term of $a+1$.

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

Combine $2a$ and $-a$ to get $a$.

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

To find the opposite of $2a^{2}+a-1$, find the opposite of each term.

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

The opposite of $-1$ is $1$.

$$2a^{2}-a-1-2a^{2}-a+1$$

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

$$-a-1-a+1$$

Combine $-a$ and $-a$ to get $-2a$.

$$-2a-1+1$$

Add $-1$ and $1$ to get $0$.

$$-2a$$

Expand

$-2a$

Solution Steps

Apply the distributive property by multiplying each term of $a-1$ by each term of $2a+1$.

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

Combine $a$ and $-2a$ to get $-a$.

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

Apply the distributive property by multiplying each term of $2a-1$ by each term of $a+1$.

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

Combine $2a$ and $-a$ to get $a$.

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

To find the opposite of $2a^{2}+a-1$, find the opposite of each term.

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

The opposite of $-1$ is $1$.

$$2a^{2}-a-1-2a^{2}-a+1$$

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

$$-a-1-a+1$$

Combine $-a$ and $-a$ to get $-2a$.

$$-2a-1+1$$

Add $-1$ and $1$ to get $0$.

$$-2a$$