Basic Math Examples

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

Step 1

Simplify each term.

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Step 1.1

Rewrite ${(y + 2)}^{2}$ as $(y + 2) (y + 2)$ .

$- ((y + 2) (y + 2)) - y (2 y + 3)$

Step 1.2

Expand $(y + 2) (y + 2)$ using the FOIL Method.

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Step 1.2.1

Apply the distributive property.

$- (y (y + 2) + 2 (y + 2)) - y (2 y + 3)$

Step 1.2.2

Apply the distributive property.

$- (y \cdot y + y \cdot 2 + 2 (y + 2)) - y (2 y + 3)$

Step 1.2.3

Apply the distributive property.

$- (y \cdot y + y \cdot 2 + 2 y + 2 \cdot 2) - y (2 y + 3)$

Step 1.3

Simplify and combine like terms.

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Step 1.3.1

Simplify each term.

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Step 1.3.1.1

Multiply $y$ by $y$ .

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

Step 1.3.1.2

Move $2$ to the left of $y$ .

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

Step 1.3.1.3

Multiply $2$ by $2$ .

$- (y^{2} + 2 y + 2 y + 4) - y (2 y + 3)$

Step 1.3.2

Add $2 y$ and $2 y$ .

$- (y^{2} + 4 y + 4) - y (2 y + 3)$

Step 1.4

Apply the distributive property.

$- y^{2} - (4 y) - 1 \cdot 4 - y (2 y + 3)$

Step 1.5

Simplify.

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Step 1.5.1

Multiply $4$ by $- 1$ .

$- y^{2} - 4 y - 1 \cdot 4 - y (2 y + 3)$

Step 1.5.2

Multiply $- 1$ by $4$ .

$- y^{2} - 4 y - 4 - y (2 y + 3)$

Step 1.6

Apply the distributive property.

$- y^{2} - 4 y - 4 - y (2 y) - y \cdot 3$

Step 1.7

Rewrite using the commutative property of multiplication.

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

Step 1.8

Multiply $3$ by $- 1$ .

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

Step 1.9

Simplify each term.

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Step 1.9.1

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

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Step 1.9.1.1

Move $y$ .

$- y^{2} - 4 y - 4 - 1 \cdot 2 (y \cdot y) - 3 y$

Step 1.9.1.2

Multiply $y$ by $y$ .

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

Step 1.9.2

Multiply $- 1$ by $2$ .

$- y^{2} - 4 y - 4 - 2 y^{2} - 3 y$

Step 2

Simplify by adding terms.

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Step 2.1

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

$- 3 y^{2} - 4 y - 4 - 3 y$

Step 2.2

Subtract $3 y$ from $- 4 y$ .

$- 3 y^{2} - 7 y - 4$