Solve b(12a - 3) - (a - b)(3 + 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

$$b(12a-3)-(a-b)(3+b)$$

Evaluate

$11ab-3a+b^{2}$

Solution Steps

Use the distributive property to multiply $b$ by $12a-3$.

$$12ba-3b-\left(a-b\right)\left(3+b\right)$$

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

$$12ba-3b-\left(3a+ab-3b-b^{2}\right)$$

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

$$12ba-3b-3a-ab-\left(-3b\right)-\left(-b^{2}\right)$$

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

$$12ba-3b-3a-ab+3b-\left(-b^{2}\right)$$

The opposite of $-b^{2}$ is $b^{2}$.

$$12ba-3b-3a-ab+3b+b^{2}$$

Combine $12ba$ and $-ab$ to get $11ba$.

$$11ba-3b-3a+3b+b^{2}$$

Combine $-3b$ and $3b$ to get $0$.

$$11ba-3a+b^{2}$$

Expand

$11ab-3a+b^{2}$

Solution Steps

Use the distributive property to multiply $b$ by $12a-3$.

$$12ba-3b-\left(a-b\right)\left(3+b\right)$$

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

$$12ba-3b-\left(3a+ab-3b-b^{2}\right)$$

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

$$12ba-3b-3a-ab-\left(-3b\right)-\left(-b^{2}\right)$$

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

$$12ba-3b-3a-ab+3b-\left(-b^{2}\right)$$

The opposite of $-b^{2}$ is $b^{2}$.

$$12ba-3b-3a-ab+3b+b^{2}$$

Combine $12ba$ and $-ab$ to get $11ba$.

$$11ba-3b-3a+3b+b^{2}$$

Combine $-3b$ and $3b$ to get $0$.

$$11ba-3a+b^{2}$$