Algebra Examples

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

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

$b a + b \cdot b - a (a - b)$

Step 1.2

Multiply $b$ by $b$ .

$b a + b^{2} - a (a - b)$

Step 1.3

Apply the distributive property.

$b a + b^{2} - a \cdot a - a (- b)$

Step 1.4

Multiply $a$ by $a$ by adding the exponents.

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Step 1.4.1

Move $a$ .

$b a + b^{2} - (a \cdot a) - a (- b)$

Step 1.4.2

Multiply $a$ by $a$ .

$b a + b^{2} - a^{2} - a (- b)$

$b a + b^{2} - a^{2} - a (- b)$

Step 1.5

Rewrite using the commutative property of multiplication.

$b a + b^{2} - a^{2} - 1 \cdot - 1 a b$

Step 1.6

Simplify each term.

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Step 1.6.1

Multiply $- 1$ by $- 1$ .

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

Step 1.6.2

Multiply $a$ by $1$ .

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

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

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

Step 2

Add $b a$ and $a b$ .

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Step 2.1

Reorder $b$ and $a$ .

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

Step 2.2

Add $a b$ and $a b$ .

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

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

Step 3

Move $b^{2}$ .

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

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$