Basic Math Examples

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

Step 1

Simplify each term.

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Step 1.1

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

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

Step 1.2

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

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Step 1.2.1

Apply the distributive property.

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

Step 1.2.2

Apply the distributive property.

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

Step 1.2.3

Apply the distributive property.

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

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 $a$ by $a$ .

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

Step 1.3.1.2

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

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

Step 1.3.1.3

Multiply $7$ by $7$ .

$a^{2} + 7 a + 7 a + 49 - {(a - 7)}^{2}$

Step 1.3.2

Add $7 a$ and $7 a$ .

$a^{2} + 14 a + 49 - {(a - 7)}^{2}$

Step 1.4

Rewrite ${(a - 7)}^{2}$ as $(a - 7) (a - 7)$ .

$a^{2} + 14 a + 49 - ((a - 7) (a - 7))$

Step 1.5

Expand $(a - 7) (a - 7)$ using the FOIL Method.

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Step 1.5.1

Apply the distributive property.

$a^{2} + 14 a + 49 - (a (a - 7) - 7 (a - 7))$

Step 1.5.2

Apply the distributive property.

$a^{2} + 14 a + 49 - (a \cdot a + a \cdot - 7 - 7 (a - 7))$

Step 1.5.3

Apply the distributive property.

$a^{2} + 14 a + 49 - (a \cdot a + a \cdot - 7 - 7 a - 7 \cdot - 7)$

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 $a$ by $a$ .

$a^{2} + 14 a + 49 - (a^{2} + a \cdot - 7 - 7 a - 7 \cdot - 7)$

Step 1.6.1.2

Move $- 7$ to the left of $a$ .

$a^{2} + 14 a + 49 - (a^{2} - 7 \cdot a - 7 a - 7 \cdot - 7)$

Step 1.6.1.3

Multiply $- 7$ by $- 7$ .

$a^{2} + 14 a + 49 - (a^{2} - 7 a - 7 a + 49)$

Step 1.6.2

Subtract $7 a$ from $- 7 a$ .

$a^{2} + 14 a + 49 - (a^{2} - 14 a + 49)$

Step 1.7

Apply the distributive property.

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

Step 1.8

Simplify.

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Step 1.8.1

Multiply $- 14$ by $- 1$ .

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

Step 1.8.2

Multiply $- 1$ by $49$ .

$a^{2} + 14 a + 49 - a^{2} + 14 a - 49$

Step 2

Simplify by adding terms.

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Step 2.1

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

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Step 2.1.1

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

$14 a + 49 + 0 + 14 a - 49$

Step 2.1.2

Add $14 a + 49$ and $0$ .

$14 a + 49 + 14 a - 49$

Step 2.1.3

Subtract $49$ from $49$ .

$14 a + 14 a + 0$

Step 2.1.4

Add $14 a + 14 a$ and $0$ .

$14 a + 14 a$

Step 2.2

Add $14 a$ and $14 a$ .

$28 a$