Basic Math Examples

$(8 - a) (7 - a) (3 - a)$

Step 1

Expand $(8 - a) (7 - a)$ using the FOIL Method.

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Step 1.1

Apply the distributive property.

$(8 (7 - a) - a (7 - a)) (3 - a)$

Step 1.2

Apply the distributive property.

$(8 \cdot 7 + 8 (- a) - a (7 - a)) (3 - a)$

Step 1.3

Apply the distributive property.

$(8 \cdot 7 + 8 (- a) - a \cdot 7 - a (- a)) (3 - a)$

Step 2

Simplify and combine like terms.

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Step 2.1

Simplify each term.

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Step 2.1.1

Multiply $8$ by $7$ .

$(56 + 8 (- a) - a \cdot 7 - a (- a)) (3 - a)$

Step 2.1.2

Multiply $- 1$ by $8$ .

$(56 - 8 a - a \cdot 7 - a (- a)) (3 - a)$

Step 2.1.3

Multiply $7$ by $- 1$ .

$(56 - 8 a - 7 a - a (- a)) (3 - a)$

Step 2.1.4

Rewrite using the commutative property of multiplication.

$(56 - 8 a - 7 a - 1 \cdot - 1 a \cdot a) (3 - a)$

Step 2.1.5

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

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Step 2.1.5.1

Move $a$ .

$(56 - 8 a - 7 a - 1 \cdot - 1 (a \cdot a)) (3 - a)$

Step 2.1.5.2

Multiply $a$ by $a$ .

$(56 - 8 a - 7 a - 1 \cdot - 1 a^{2}) (3 - a)$

Step 2.1.6

Multiply $- 1$ by $- 1$ .

$(56 - 8 a - 7 a + 1 a^{2}) (3 - a)$

Step 2.1.7

Multiply $a^{2}$ by $1$ .

$(56 - 8 a - 7 a + a^{2}) (3 - a)$

Step 2.2

Subtract $7 a$ from $- 8 a$ .

$(56 - 15 a + a^{2}) (3 - a)$

Step 3

Expand $(56 - 15 a + a^{2}) (3 - a)$ by multiplying each term in the first expression by each term in the second expression.

$56 \cdot 3 + 56 (- a) - 15 a \cdot 3 - 15 a (- a) + a^{2} \cdot 3 + a^{2} (- a)$

Step 4

Simplify terms.

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Step 4.1

Simplify each term.

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Step 4.1.1

Multiply $56$ by $3$ .

$168 + 56 (- a) - 15 a \cdot 3 - 15 a (- a) + a^{2} \cdot 3 + a^{2} (- a)$

Step 4.1.2

Multiply $- 1$ by $56$ .

$168 - 56 a - 15 a \cdot 3 - 15 a (- a) + a^{2} \cdot 3 + a^{2} (- a)$

Step 4.1.3

Multiply $3$ by $- 15$ .

$168 - 56 a - 45 a - 15 a (- a) + a^{2} \cdot 3 + a^{2} (- a)$

Step 4.1.4

Rewrite using the commutative property of multiplication.

$168 - 56 a - 45 a - 15 \cdot - 1 a \cdot a + a^{2} \cdot 3 + a^{2} (- a)$

Step 4.1.5

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

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Step 4.1.5.1

Move $a$ .

$168 - 56 a - 45 a - 15 \cdot - 1 (a \cdot a) + a^{2} \cdot 3 + a^{2} (- a)$

Step 4.1.5.2

Multiply $a$ by $a$ .

$168 - 56 a - 45 a - 15 \cdot - 1 a^{2} + a^{2} \cdot 3 + a^{2} (- a)$

Step 4.1.6

Multiply $- 15$ by $- 1$ .

$168 - 56 a - 45 a + 15 a^{2} + a^{2} \cdot 3 + a^{2} (- a)$

Step 4.1.7

Move $3$ to the left of $a^{2}$ .

$168 - 56 a - 45 a + 15 a^{2} + 3 \cdot a^{2} + a^{2} (- a)$

Step 4.1.8

Rewrite using the commutative property of multiplication.

$168 - 56 a - 45 a + 15 a^{2} + 3 a^{2} - a^{2} a$

Step 4.1.9

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

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Step 4.1.9.1

Move $a$ .

$168 - 56 a - 45 a + 15 a^{2} + 3 a^{2} - (a \cdot a^{2})$

Step 4.1.9.2

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

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Step 4.1.9.2.1

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

$168 - 56 a - 45 a + 15 a^{2} + 3 a^{2} - (a^{1} a^{2})$

Step 4.1.9.2.2

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

$168 - 56 a - 45 a + 15 a^{2} + 3 a^{2} - a^{1 + 2}$

Step 4.1.9.3

Add $1$ and $2$ .

$168 - 56 a - 45 a + 15 a^{2} + 3 a^{2} - a^{3}$

Step 4.2

Simplify by adding terms.

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Step 4.2.1

Subtract $45 a$ from $- 56 a$ .

$168 - 101 a + 15 a^{2} + 3 a^{2} - a^{3}$

Step 4.2.2

Add $15 a^{2}$ and $3 a^{2}$ .

$168 - 101 a + 18 a^{2} - a^{3}$