Basic Math Examples

${(w + 2)}^{2} - {(w + 7)}^{2}$

Step 1

Simplify each term.

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Step 1.1

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

$(w + 2) (w + 2) - {(w + 7)}^{2}$

Step 1.2

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

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Step 1.2.1

Apply the distributive property.

$w (w + 2) + 2 (w + 2) - {(w + 7)}^{2}$

Step 1.2.2

Apply the distributive property.

$w \cdot w + w \cdot 2 + 2 (w + 2) - {(w + 7)}^{2}$

Step 1.2.3

Apply the distributive property.

$w \cdot w + w \cdot 2 + 2 w + 2 \cdot 2 - {(w + 7)}^{2}$

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 $w$ by $w$ .

$w^{2} + w \cdot 2 + 2 w + 2 \cdot 2 - {(w + 7)}^{2}$

Step 1.3.1.2

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

$w^{2} + 2 \cdot w + 2 w + 2 \cdot 2 - {(w + 7)}^{2}$

Step 1.3.1.3

Multiply $2$ by $2$ .

$w^{2} + 2 w + 2 w + 4 - {(w + 7)}^{2}$

Step 1.3.2

Add $2 w$ and $2 w$ .

$w^{2} + 4 w + 4 - {(w + 7)}^{2}$

Step 1.4

Rewrite ${(w + 7)}^{2}$ as $(w + 7) (w + 7)$ .

$w^{2} + 4 w + 4 - ((w + 7) (w + 7))$

Step 1.5

Expand $(w + 7) (w + 7)$ using the FOIL Method.

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Step 1.5.1

Apply the distributive property.

$w^{2} + 4 w + 4 - (w (w + 7) + 7 (w + 7))$

Step 1.5.2

Apply the distributive property.

$w^{2} + 4 w + 4 - (w \cdot w + w \cdot 7 + 7 (w + 7))$

Step 1.5.3

Apply the distributive property.

$w^{2} + 4 w + 4 - (w \cdot w + w \cdot 7 + 7 w + 7 \cdot 7)$

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 $w$ by $w$ .

$w^{2} + 4 w + 4 - (w^{2} + w \cdot 7 + 7 w + 7 \cdot 7)$

Step 1.6.1.2

Move $7$ to the left of $w$ .

$w^{2} + 4 w + 4 - (w^{2} + 7 \cdot w + 7 w + 7 \cdot 7)$

Step 1.6.1.3

Multiply $7$ by $7$ .

$w^{2} + 4 w + 4 - (w^{2} + 7 w + 7 w + 49)$

Step 1.6.2

Add $7 w$ and $7 w$ .

$w^{2} + 4 w + 4 - (w^{2} + 14 w + 49)$

Step 1.7

Apply the distributive property.

$w^{2} + 4 w + 4 - w^{2} - (14 w) - 1 \cdot 49$

Step 1.8

Simplify.

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Step 1.8.1

Multiply $14$ by $- 1$ .

$w^{2} + 4 w + 4 - w^{2} - 14 w - 1 \cdot 49$

Step 1.8.2

Multiply $- 1$ by $49$ .

$w^{2} + 4 w + 4 - w^{2} - 14 w - 49$

Step 2

Simplify by adding terms.

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Step 2.1

Combine the opposite terms in $w^{2} + 4 w + 4 - w^{2} - 14 w - 49$ .

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Step 2.1.1

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

$4 w + 4 + 0 - 14 w - 49$

Step 2.1.2

Add $4 w + 4$ and $0$ .

$4 w + 4 - 14 w - 49$

Step 2.2

Subtract $14 w$ from $4 w$ .

$- 10 w + 4 - 49$

Step 2.3

Subtract $49$ from $4$ .

$- 10 w - 45$