Basic Math Examples

$(9 w + y) (4 - 2 w)$

Step 1

Expand $(9 w + y) (4 - 2 w)$ using the FOIL Method.

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Step 1.1

Apply the distributive property.

$9 w (4 - 2 w) + y (4 - 2 w)$

Step 1.2

Apply the distributive property.

$9 w \cdot 4 + 9 w (- 2 w) + y (4 - 2 w)$

Step 1.3

Apply the distributive property.

$9 w \cdot 4 + 9 w (- 2 w) + y \cdot 4 + y (- 2 w)$

Step 2

Simplify terms.

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Step 2.1

Simplify each term.

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Step 2.1.1

Multiply $4$ by $9$ .

$36 w + 9 w (- 2 w) + y \cdot 4 + y (- 2 w)$

Step 2.1.2

Rewrite using the commutative property of multiplication.

$36 w + 9 \cdot - 2 w \cdot w + y \cdot 4 + y (- 2 w)$

Step 2.1.3

Multiply $w$ by $w$ by adding the exponents.

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Step 2.1.3.1

Move $w$ .

$36 w + 9 \cdot - 2 (w \cdot w) + y \cdot 4 + y (- 2 w)$

Step 2.1.3.2

Multiply $w$ by $w$ .

$36 w + 9 \cdot - 2 w^{2} + y \cdot 4 + y (- 2 w)$

Step 2.1.4

Multiply $9$ by $- 2$ .

$36 w - 18 w^{2} + y \cdot 4 + y (- 2 w)$

Step 2.1.5

Move $4$ to the left of $y$ .

$36 w - 18 w^{2} + 4 \cdot y + y (- 2 w)$

Step 2.1.6

Rewrite using the commutative property of multiplication.

$36 w - 18 w^{2} + 4 y - 2 y w$

Step 2.2

Simplify the expression.

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Step 2.2.1

Move $y$ .

$36 w - 18 w^{2} + 4 y - 2 w y$

Step 2.2.2

Move $36 w$ .

$- 18 w^{2} + 4 y - 2 w y + 36 w$

Step 2.2.3

Move $4 y$ .

$- 18 w^{2} - 2 w y + 4 y + 36 w$

Step 2.2.4

Reorder $- 18 w^{2}$ and $- 2 w y$ .

$- 2 w y - 18 w^{2} + 4 y + 36 w$