Basic Math Examples

$\frac{5 + {(1 - 2 a + 8)}^{2}}{2} \cdot (- 2 a + 8)$

Step 1

Simplify the numerator.

Tap for more steps...

Step 1.1

Add $1$ and $8$ .

$\frac{5 + {(- 2 a + 9)}^{2}}{2} \cdot (- 2 a + 8)$

Step 1.2

Rewrite ${(- 2 a + 9)}^{2}$ as $(- 2 a + 9) (- 2 a + 9)$ .

$\frac{5 + (- 2 a + 9) (- 2 a + 9)}{2} \cdot (- 2 a + 8)$

Step 1.3

Expand $(- 2 a + 9) (- 2 a + 9)$ using the FOIL Method.

Tap for more steps...

Step 1.3.1

Apply the distributive property.

$\frac{5 - 2 a (- 2 a + 9) + 9 (- 2 a + 9)}{2} \cdot (- 2 a + 8)$

Step 1.3.2

Apply the distributive property.

$\frac{5 - 2 a (- 2 a) - 2 a \cdot 9 + 9 (- 2 a + 9)}{2} \cdot (- 2 a + 8)$

Step 1.3.3

Apply the distributive property.

$\frac{5 - 2 a (- 2 a) - 2 a \cdot 9 + 9 (- 2 a) + 9 \cdot 9}{2} \cdot (- 2 a + 8)$

Step 1.4

Simplify and combine like terms.

Tap for more steps...

Step 1.4.1

Simplify each term.

Tap for more steps...

Step 1.4.1.1

Rewrite using the commutative property of multiplication.

$\frac{5 - 2 \cdot - 2 a \cdot a - 2 a \cdot 9 + 9 (- 2 a) + 9 \cdot 9}{2} \cdot (- 2 a + 8)$

Step 1.4.1.2

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

Tap for more steps...

Step 1.4.1.2.1

Move $a$ .

$\frac{5 - 2 \cdot - 2 (a \cdot a) - 2 a \cdot 9 + 9 (- 2 a) + 9 \cdot 9}{2} \cdot (- 2 a + 8)$

Step 1.4.1.2.2

Multiply $a$ by $a$ .

$\frac{5 - 2 \cdot - 2 a^{2} - 2 a \cdot 9 + 9 (- 2 a) + 9 \cdot 9}{2} \cdot (- 2 a + 8)$

Step 1.4.1.3

Multiply $- 2$ by $- 2$ .

$\frac{5 + 4 a^{2} - 2 a \cdot 9 + 9 (- 2 a) + 9 \cdot 9}{2} \cdot (- 2 a + 8)$

Step 1.4.1.4

Multiply $9$ by $- 2$ .

$\frac{5 + 4 a^{2} - 18 a + 9 (- 2 a) + 9 \cdot 9}{2} \cdot (- 2 a + 8)$

Step 1.4.1.5

Multiply $- 2$ by $9$ .

$\frac{5 + 4 a^{2} - 18 a - 18 a + 9 \cdot 9}{2} \cdot (- 2 a + 8)$

Step 1.4.1.6

Multiply $9$ by $9$ .

$\frac{5 + 4 a^{2} - 18 a - 18 a + 81}{2} \cdot (- 2 a + 8)$

Step 1.4.2

Subtract $18 a$ from $- 18 a$ .

$\frac{5 + 4 a^{2} - 36 a + 81}{2} \cdot (- 2 a + 8)$

Step 1.5

Add $5$ and $81$ .

$\frac{4 a^{2} - 36 a + 86}{2} \cdot (- 2 a + 8)$

Step 1.6

Factor $2$ out of $4 a^{2} - 36 a + 86$ .

Tap for more steps...

Step 1.6.1

Factor $2$ out of $4 a^{2}$ .

$\frac{2 (2 a^{2}) - 36 a + 86}{2} \cdot (- 2 a + 8)$

Step 1.6.2

Factor $2$ out of $- 36 a$ .

$\frac{2 (2 a^{2}) + 2 (- 18 a) + 86}{2} \cdot (- 2 a + 8)$

Step 1.6.3

Factor $2$ out of $86$ .

$\frac{2 (2 a^{2}) + 2 (- 18 a) + 2 (43)}{2} \cdot (- 2 a + 8)$

Step 1.6.4

Factor $2$ out of $2 (2 a^{2}) + 2 (- 18 a)$ .

$\frac{2 (2 a^{2} - 18 a) + 2 (43)}{2} \cdot (- 2 a + 8)$

Step 1.6.5

Factor $2$ out of $2 (2 a^{2} - 18 a) + 2 (43)$ .

$\frac{2 (2 a^{2} - 18 a + 43)}{2} \cdot (- 2 a + 8)$

Step 2

Cancel the common factor of $2$ .

Tap for more steps...

Step 2.1

Cancel the common factor.

$\frac{2 (2 a^{2} - 18 a + 43)}{2} \cdot (- 2 a + 8)$

Step 2.2

Divide $2 a^{2} - 18 a + 43$ by $1$ .

$(2 a^{2} - 18 a + 43) \cdot (- 2 a + 8)$

Step 3

Expand $(2 a^{2} - 18 a + 43) (- 2 a + 8)$ by multiplying each term in the first expression by each term in the second expression.

$2 a^{2} (- 2 a) + 2 a^{2} \cdot 8 - 18 a (- 2 a) - 18 a \cdot 8 + 43 (- 2 a) + 43 \cdot 8$

Step 4

Simplify terms.

Tap for more steps...

Step 4.1

Simplify each term.

Tap for more steps...

Step 4.1.1

Rewrite using the commutative property of multiplication.

$2 \cdot - 2 a^{2} a + 2 a^{2} \cdot 8 - 18 a (- 2 a) - 18 a \cdot 8 + 43 (- 2 a) + 43 \cdot 8$

Step 4.1.2

Multiply $a^{2}$ by $a$ by adding the exponents.

Tap for more steps...

Step 4.1.2.1

Move $a$ .

$2 \cdot - 2 (a \cdot a^{2}) + 2 a^{2} \cdot 8 - 18 a (- 2 a) - 18 a \cdot 8 + 43 (- 2 a) + 43 \cdot 8$

Step 4.1.2.2

Multiply $a$ by $a^{2}$ .

Tap for more steps...

Step 4.1.2.2.1

Raise $a$ to the power of $1$ .

$2 \cdot - 2 (a^{1} a^{2}) + 2 a^{2} \cdot 8 - 18 a (- 2 a) - 18 a \cdot 8 + 43 (- 2 a) + 43 \cdot 8$

Step 4.1.2.2.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$2 \cdot - 2 a^{1 + 2} + 2 a^{2} \cdot 8 - 18 a (- 2 a) - 18 a \cdot 8 + 43 (- 2 a) + 43 \cdot 8$

Step 4.1.2.3

Add $1$ and $2$ .

$2 \cdot - 2 a^{3} + 2 a^{2} \cdot 8 - 18 a (- 2 a) - 18 a \cdot 8 + 43 (- 2 a) + 43 \cdot 8$

Step 4.1.3

Multiply $2$ by $- 2$ .

$- 4 a^{3} + 2 a^{2} \cdot 8 - 18 a (- 2 a) - 18 a \cdot 8 + 43 (- 2 a) + 43 \cdot 8$

Step 4.1.4

Multiply $8$ by $2$ .

$- 4 a^{3} + 16 a^{2} - 18 a (- 2 a) - 18 a \cdot 8 + 43 (- 2 a) + 43 \cdot 8$

Step 4.1.5

Rewrite using the commutative property of multiplication.

$- 4 a^{3} + 16 a^{2} - 18 \cdot - 2 a \cdot a - 18 a \cdot 8 + 43 (- 2 a) + 43 \cdot 8$

Step 4.1.6

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

Tap for more steps...

Step 4.1.6.1

Move $a$ .

$- 4 a^{3} + 16 a^{2} - 18 \cdot - 2 (a \cdot a) - 18 a \cdot 8 + 43 (- 2 a) + 43 \cdot 8$

Step 4.1.6.2

Multiply $a$ by $a$ .

$- 4 a^{3} + 16 a^{2} - 18 \cdot - 2 a^{2} - 18 a \cdot 8 + 43 (- 2 a) + 43 \cdot 8$

Step 4.1.7

Multiply $- 18$ by $- 2$ .

$- 4 a^{3} + 16 a^{2} + 36 a^{2} - 18 a \cdot 8 + 43 (- 2 a) + 43 \cdot 8$

Step 4.1.8

Multiply $8$ by $- 18$ .

$- 4 a^{3} + 16 a^{2} + 36 a^{2} - 144 a + 43 (- 2 a) + 43 \cdot 8$

Step 4.1.9

Multiply $- 2$ by $43$ .

$- 4 a^{3} + 16 a^{2} + 36 a^{2} - 144 a - 86 a + 43 \cdot 8$

Step 4.1.10

Multiply $43$ by $8$ .

$- 4 a^{3} + 16 a^{2} + 36 a^{2} - 144 a - 86 a + 344$

Step 4.2

Simplify by adding terms.

Tap for more steps...

Step 4.2.1

Add $16 a^{2}$ and $36 a^{2}$ .

$- 4 a^{3} + 52 a^{2} - 144 a - 86 a + 344$

Step 4.2.2

Subtract $86 a$ from $- 144 a$ .

$- 4 a^{3} + 52 a^{2} - 230 a + 344$