Pre-Algebra Examples

$a (3 a + 1) + (a + 1) (a - 1)$

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

$a (3 a) + a \cdot 1 + (a + 1) (a - 1)$

Step 1.2

Rewrite using the commutative property of multiplication.

$3 a \cdot a + a \cdot 1 + (a + 1) (a - 1)$

Step 1.3

Multiply $a$ by $1$ .

$3 a \cdot a + a + (a + 1) (a - 1)$

Step 1.4

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

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Step 1.4.1

Move $a$ .

$3 (a \cdot a) + a + (a + 1) (a - 1)$

Step 1.4.2

Multiply $a$ by $a$ .

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

Step 1.5

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

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Step 1.5.1

Apply the distributive property.

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

Step 1.5.2

Apply the distributive property.

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

Step 1.5.3

Apply the distributive property.

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

Step 1.6

Simplify and combine like terms.

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Step 1.6.1

Simplify each term.

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Step 1.6.1.1

Multiply $a$ by $a$ .

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

Step 1.6.1.2

Move $- 1$ to the left of $a$ .

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

Step 1.6.1.3

Rewrite $- 1 a$ as $- a$ .

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

Step 1.6.1.4

Multiply $a$ by $1$ .

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

Step 1.6.1.5

Multiply $- 1$ by $1$ .

$3 a^{2} + a + a^{2} - a + a - 1$

Step 1.6.2

Add $- a$ and $a$ .

$3 a^{2} + a + a^{2} + 0 - 1$

Step 1.6.3

Add $a^{2}$ and $0$ .

$3 a^{2} + a + a^{2} - 1$

Step 2

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

$4 a^{2} + a - 1$