Solve (3a-1)(b+2)-(1-3a)(b-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

$$(3a-1)(b+2)-(1-3a)(b-2)=$$

Evaluate

$6ab-2b$

Solution Steps

Apply the distributive property by multiplying each term of $3a-1$ by each term of $b+2$.

$$3ab+6a-b-2-\left(1-3a\right)\left(b-2\right)$$

Apply the distributive property by multiplying each term of $1-3a$ by each term of $b-2$.

$$3ab+6a-b-2-\left(b-2-3ab+6a\right)$$

To find the opposite of $b-2-3ab+6a$, find the opposite of each term.

$$3ab+6a-b-2-b-\left(-2\right)-\left(-3ab\right)-6a$$

The opposite of $-2$ is $2$.

$$3ab+6a-b-2-b+2-\left(-3ab\right)-6a$$

The opposite of $-3ab$ is $3ab$.

$$3ab+6a-b-2-b+2+3ab-6a$$

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

$$3ab+6a-2b-2+2+3ab-6a$$

Add $-2$ and $2$ to get $0$.

$$3ab+6a-2b+3ab-6a$$

Combine $6a$ and $-6a$ to get $0$.

$$3ab-2b+3ab$$

Combine $3ab$ and $3ab$ to get $6ab$.

$$6ab-2b$$

Expand

$6ab-2b$

Solution Steps

Apply the distributive property by multiplying each term of $3a-1$ by each term of $b+2$.

$$3ab+6a-b-2-\left(1-3a\right)\left(b-2\right)$$

Apply the distributive property by multiplying each term of $1-3a$ by each term of $b-2$.

$$3ab+6a-b-2-\left(b-2-3ab+6a\right)$$

To find the opposite of $b-2-3ab+6a$, find the opposite of each term.

$$3ab+6a-b-2-b-\left(-2\right)-\left(-3ab\right)-6a$$

The opposite of $-2$ is $2$.

$$3ab+6a-b-2-b+2-\left(-3ab\right)-6a$$

The opposite of $-3ab$ is $3ab$.

$$3ab+6a-b-2-b+2+3ab-6a$$

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

$$3ab+6a-2b-2+2+3ab-6a$$

Add $-2$ and $2$ to get $0$.

$$3ab+6a-2b+3ab-6a$$

Combine $6a$ and $-6a$ to get $0$.

$$3ab-2b+3ab$$

Combine $3ab$ and $3ab$ to get $6ab$.

$$6ab-2b$$