Algebra Examples

$(a \cdot 4 + 4 b \cdot 4) \div (a \cdot 2 - 2 a b + 2 b \cdot 2)$

Step 1

Expand $a \cdot 4 + 4 b \cdot 4$ .

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Step 1.1

Reorder $a$ and $4$ .

$\frac{4 \cdot a + 4 b \cdot 4}{a \cdot 2 - 2 a b + 2 b \cdot 2}$

Step 1.2

Move $b$ .

$\frac{4 a + 4 \cdot (4 b)}{a \cdot 2 - 2 a b + 2 b \cdot 2}$

Step 1.3

Multiply $4$ by $4$ .

$\frac{4 a + 16 b}{a \cdot 2 - 2 a b + 2 b \cdot 2}$

Step 2

Expand $a \cdot 2 - 2 a b + 2 b \cdot 2$ .

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Step 2.1

Reorder $a$ and $2$ .

$\frac{4 a + 16 b}{2 \cdot a - 2 a b + 2 b \cdot 2}$

Step 2.2

Move $b$ .

$\frac{4 a + 16 b}{2 a - 2 a b + 2 \cdot (2 b)}$

Step 2.3

Multiply $2$ by $2$ .

$\frac{4 a + 16 b}{2 a - 2 a b + 4 b}$

Step 2.4

Move $- 2 a b$ .

$\frac{4 a + 16 b}{2 a + 4 b - 2 a b}$

Step 3

Set up the polynomials to be divided. If there is not a term for every exponent, insert one with a value of $0$ .

$2 a$

$2 a b$

$4 b$

$4 a$

$16 b$

Step 4

Divide the highest order term in the dividend $4 a$ by the highest order term in divisor $2 a$ .

							$2$
	$2 a$	-	$2 a b$	+	$4 b$		$4 a$	+	$16 b$

Step 5

Multiply the new quotient term by the divisor.

						$2$
$2 a$	-	$2 a b$	+	$4 b$		$4 a$	+	$16 b$
					+	$4 a$	-	$4 a b$	+	$8 b$

Step 6

The expression needs to be subtracted from the dividend, so change all the signs in $4 a - 4 a b + 8 b$

						$2$
$2 a$	-	$2 a b$	+	$4 b$		$4 a$	+	$16 b$
					-	$4 a$	+	$4 a b$	-	$8 b$

Step 7

After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.

						$2$
$2 a$	-	$2 a b$	+	$4 b$		$4 a$	+	$16 b$
					-	$4 a$	+	$4 a b$	-	$8 b$
							+	$16 b$	-	$8 b$

Step 8

The final answer is the quotient plus the remainder over the divisor.

$2 + \frac{8 b}{2 a - 2 a b + 4 b}$