Solve a ( a b ) - b( a 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

$$a ( a - b ) - b ( a - b )$$

Evaluate

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

Solution Steps

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

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

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

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

To find the opposite of $ba-b^{2}$, find the opposite of each term.

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

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

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

Combine $-ab$ and $-ba$ to get $-2ab$.

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

Expand

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

Solution Steps

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

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

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

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

To find the opposite of $ba-b^{2}$, find the opposite of each term.

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

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

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

Combine $-ab$ and $-ba$ to get $-2ab$.

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