Basic Math Examples

$(y^{2} - y + 3) (y + 2)$

Step 1

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

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

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

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

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Step 2.1.1.1.1

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

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

Step 2.1.1.1.2

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

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

Step 2.1.1.2

Add $2$ and $1$ .

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

Step 2.1.2

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

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

Step 2.1.3

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

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Step 2.1.3.1

Move $y$ .

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

Step 2.1.3.2

Multiply $y$ by $y$ .

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

Step 2.1.4

Multiply $2$ by $- 1$ .

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

Step 2.1.5

Multiply $3$ by $2$ .

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

Step 2.2

Simplify by adding terms.

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Step 2.2.1

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

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

Step 2.2.2

Add $- 2 y$ and $3 y$ .

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