Algebra Examples

$(a^{2} - 7) (a + 2) - (2 a - 1) (a - 14)$

Step 1

Simplify each term.

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Step 1.1

Expand $(a^{2} - 7) (a + 2)$ using the FOIL Method.

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Step 1.1.1

Apply the distributive property.

$a^{2} (a + 2) - 7 (a + 2) - (2 a - 1) (a - 14)$

Step 1.1.2

Apply the distributive property.

$a^{2} a + a^{2} \cdot 2 - 7 (a + 2) - (2 a - 1) (a - 14)$

Step 1.1.3

Apply the distributive property.

$a^{2} a + a^{2} \cdot 2 - 7 a - 7 \cdot 2 - (2 a - 1) (a - 14)$

Step 1.2

Simplify each term.

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Step 1.2.1

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

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Step 1.2.1.1

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

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Step 1.2.1.1.1

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

$a^{2} a^{1} + a^{2} \cdot 2 - 7 a - 7 \cdot 2 - (2 a - 1) (a - 14)$

Step 1.2.1.1.2

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

$a^{2 + 1} + a^{2} \cdot 2 - 7 a - 7 \cdot 2 - (2 a - 1) (a - 14)$

Step 1.2.1.2

Add $2$ and $1$ .

$a^{3} + a^{2} \cdot 2 - 7 a - 7 \cdot 2 - (2 a - 1) (a - 14)$

Step 1.2.2

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

$a^{3} + 2 \cdot a^{2} - 7 a - 7 \cdot 2 - (2 a - 1) (a - 14)$

Step 1.2.3

Multiply $- 7$ by $2$ .

$a^{3} + 2 a^{2} - 7 a - 14 - (2 a - 1) (a - 14)$

Step 1.3

Apply the distributive property.

$a^{3} + 2 a^{2} - 7 a - 14 + (- (2 a) - - 1) (a - 14)$

Step 1.4

Multiply $2$ by $- 1$ .

$a^{3} + 2 a^{2} - 7 a - 14 + (- 2 a - - 1) (a - 14)$

Step 1.5

Multiply $- 1$ by $- 1$ .

$a^{3} + 2 a^{2} - 7 a - 14 + (- 2 a + 1) (a - 14)$

Step 1.6

Expand $(- 2 a + 1) (a - 14)$ using the FOIL Method.

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Step 1.6.1

Apply the distributive property.

$a^{3} + 2 a^{2} - 7 a - 14 - 2 a (a - 14) + 1 (a - 14)$

Step 1.6.2

Apply the distributive property.

$a^{3} + 2 a^{2} - 7 a - 14 - 2 a \cdot a - 2 a \cdot - 14 + 1 (a - 14)$

Step 1.6.3

Apply the distributive property.

$a^{3} + 2 a^{2} - 7 a - 14 - 2 a \cdot a - 2 a \cdot - 14 + 1 a + 1 \cdot - 14$

Step 1.7

Simplify and combine like terms.

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Step 1.7.1

Simplify each term.

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Step 1.7.1.1

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

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Step 1.7.1.1.1

Move $a$ .

$a^{3} + 2 a^{2} - 7 a - 14 - 2 (a \cdot a) - 2 a \cdot - 14 + 1 a + 1 \cdot - 14$

Step 1.7.1.1.2

Multiply $a$ by $a$ .

$a^{3} + 2 a^{2} - 7 a - 14 - 2 a^{2} - 2 a \cdot - 14 + 1 a + 1 \cdot - 14$

Step 1.7.1.2

Multiply $- 14$ by $- 2$ .

$a^{3} + 2 a^{2} - 7 a - 14 - 2 a^{2} + 28 a + 1 a + 1 \cdot - 14$

Step 1.7.1.3

Multiply $a$ by $1$ .

$a^{3} + 2 a^{2} - 7 a - 14 - 2 a^{2} + 28 a + a + 1 \cdot - 14$

Step 1.7.1.4

Multiply $- 14$ by $1$ .

$a^{3} + 2 a^{2} - 7 a - 14 - 2 a^{2} + 28 a + a - 14$

Step 1.7.2

Add $28 a$ and $a$ .

$a^{3} + 2 a^{2} - 7 a - 14 - 2 a^{2} + 29 a - 14$

Step 2

Simplify by adding terms.

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Step 2.1

Combine the opposite terms in $a^{3} + 2 a^{2} - 7 a - 14 - 2 a^{2} + 29 a - 14$ .

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Step 2.1.1

Subtract $2 a^{2}$ from $2 a^{2}$ .

$a^{3} - 7 a - 14 + 0 + 29 a - 14$

Step 2.1.2

Add $a^{3} - 7 a - 14$ and $0$ .

$a^{3} - 7 a - 14 + 29 a - 14$

Step 2.2

Add $- 7 a$ and $29 a$ .

$a^{3} + 22 a - 14 - 14$

Step 2.3

Subtract $14$ from $- 14$ .

$a^{3} + 22 a - 28$