Pre-Algebra Examples

$(6 y^{2} - 2 y + 1) (y + 2)$

Step 1

Expand $(6 y^{2} - 2 y + 1) (y + 2)$ by multiplying each term in the first expression by each term in the second expression.

$6 y^{2} y + 6 y^{2} \cdot 2 - 2 y \cdot y - 2 y \cdot 2 + 1 y + 1 \cdot 2$

Step 2

Simplify terms.

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Step 2.1

Simplify each term.

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Step 2.1.1

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

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Step 2.1.1.1

Move $y$ .

$6 (y \cdot y^{2}) + 6 y^{2} \cdot 2 - 2 y \cdot y - 2 y \cdot 2 + 1 y + 1 \cdot 2$

Step 2.1.1.2

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

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Step 2.1.1.2.1

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

$6 (y^{1} y^{2}) + 6 y^{2} \cdot 2 - 2 y \cdot y - 2 y \cdot 2 + 1 y + 1 \cdot 2$

Step 2.1.1.2.2

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

$6 y^{1 + 2} + 6 y^{2} \cdot 2 - 2 y \cdot y - 2 y \cdot 2 + 1 y + 1 \cdot 2$

Step 2.1.1.3

Add $1$ and $2$ .

$6 y^{3} + 6 y^{2} \cdot 2 - 2 y \cdot y - 2 y \cdot 2 + 1 y + 1 \cdot 2$

Step 2.1.2

Multiply $2$ by $6$ .

$6 y^{3} + 12 y^{2} - 2 y \cdot y - 2 y \cdot 2 + 1 y + 1 \cdot 2$

Step 2.1.3

Multiply $y$ by $y$ by adding the exponents.

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Step 2.1.3.1

Move $y$ .

$6 y^{3} + 12 y^{2} - 2 (y \cdot y) - 2 y \cdot 2 + 1 y + 1 \cdot 2$

Step 2.1.3.2

Multiply $y$ by $y$ .

$6 y^{3} + 12 y^{2} - 2 y^{2} - 2 y \cdot 2 + 1 y + 1 \cdot 2$

Step 2.1.4

Multiply $2$ by $- 2$ .

$6 y^{3} + 12 y^{2} - 2 y^{2} - 4 y + 1 y + 1 \cdot 2$

Step 2.1.5

Multiply $y$ by $1$ .

$6 y^{3} + 12 y^{2} - 2 y^{2} - 4 y + y + 1 \cdot 2$

Step 2.1.6

Multiply $2$ by $1$ .

$6 y^{3} + 12 y^{2} - 2 y^{2} - 4 y + y + 2$

Step 2.2

Simplify by adding terms.

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Step 2.2.1

Subtract $2 y^{2}$ from $12 y^{2}$ .

$6 y^{3} + 10 y^{2} - 4 y + y + 2$

Step 2.2.2

Add $- 4 y$ and $y$ .

$6 y^{3} + 10 y^{2} - 3 y + 2$