Basic Math Examples

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

Step 1

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

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

Step 2

Expand $(a - 2) (a - 2)$ using the FOIL Method.

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Step 2.1

Apply the distributive property.

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

Step 2.2

Apply the distributive property.

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

Step 2.3

Apply the distributive property.

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

Step 3

Simplify and combine like terms.

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Step 3.1

Simplify each term.

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Step 3.1.1

Multiply $a$ by $a$ .

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

Step 3.1.2

Move $- 2$ to the left of $a$ .

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

Step 3.1.3

Multiply $- 2$ by $- 2$ .

$(a^{2} - 2 a - 2 a + 4) {(a + 2)}^{2}$

Step 3.2

Subtract $2 a$ from $- 2 a$ .

$(a^{2} - 4 a + 4) {(a + 2)}^{2}$

Step 4

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

$(a^{2} - 4 a + 4) ((a + 2) (a + 2))$

Step 5

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

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Step 5.1

Apply the distributive property.

$(a^{2} - 4 a + 4) (a (a + 2) + 2 (a + 2))$

Step 5.2

Apply the distributive property.

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

Step 5.3

Apply the distributive property.

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

Step 6

Simplify and combine like terms.

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Step 6.1

Simplify each term.

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Step 6.1.1

Multiply $a$ by $a$ .

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

Step 6.1.2

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

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

Step 6.1.3

Multiply $2$ by $2$ .

$(a^{2} - 4 a + 4) (a^{2} + 2 a + 2 a + 4)$

Step 6.2

Add $2 a$ and $2 a$ .

$(a^{2} - 4 a + 4) (a^{2} + 4 a + 4)$

Step 7

Expand $(a^{2} - 4 a + 4) (a^{2} + 4 a + 4)$ by multiplying each term in the first expression by each term in the second expression.

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

Step 8

Simplify terms.

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Step 8.1

Combine the opposite terms in $a^{2} a^{2} + a^{2} (4 a) + a^{2} \cdot 4 - 4 a \cdot a^{2} - 4 a (4 a) - 4 a \cdot 4 + 4 a^{2} + 4 (4 a) + 4 \cdot 4$ .

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Step 8.1.1

Reorder the factors in the terms $a^{2} (4 a)$ and $- 4 a \cdot a^{2}$ .

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

Step 8.1.2

Subtract $4 a^{2} a$ from $4 a^{2} a$ .

$a^{2} a^{2} + a^{2} \cdot 4 + 0 - 4 a (4 a) - 4 a \cdot 4 + 4 a^{2} + 4 (4 a) + 4 \cdot 4$

Step 8.1.3

Add $a^{2} a^{2} + a^{2} \cdot 4$ and $0$ .

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

Step 8.1.4

Reorder the factors in the terms $- 4 a \cdot 4$ and $4 (4 a)$ .

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

Step 8.1.5

Add $- 4 \cdot 4 a$ and $4 \cdot 4 a$ .

$a^{2} a^{2} + a^{2} \cdot 4 - 4 a (4 a) + 4 a^{2} + 0 + 4 \cdot 4$

Step 8.1.6

Add $a^{2} a^{2} + a^{2} \cdot 4 - 4 a (4 a) + 4 a^{2}$ and $0$ .

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

Step 8.2

Simplify each term.

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Step 8.2.1

Multiply $a^{2}$ by $a^{2}$ by adding the exponents.

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Step 8.2.1.1

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

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

Step 8.2.1.2

Add $2$ and $2$ .

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

Step 8.2.2

Move $4$ to the left of $a^{2}$ .

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

Step 8.2.3

Rewrite using the commutative property of multiplication.

$a^{4} + 4 a^{2} - 4 \cdot 4 a \cdot a + 4 a^{2} + 4 \cdot 4$

Step 8.2.4

Multiply $a$ by $a$ by adding the exponents.

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Step 8.2.4.1

Move $a$ .

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

Step 8.2.4.2

Multiply $a$ by $a$ .

$a^{4} + 4 a^{2} - 4 \cdot 4 a^{2} + 4 a^{2} + 4 \cdot 4$

Step 8.2.5

Multiply $- 4$ by $4$ .

$a^{4} + 4 a^{2} - 16 a^{2} + 4 a^{2} + 4 \cdot 4$

Step 8.2.6

Multiply $4$ by $4$ .

$a^{4} + 4 a^{2} - 16 a^{2} + 4 a^{2} + 16$

Step 8.3

Simplify by adding terms.

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Step 8.3.1

Subtract $16 a^{2}$ from $4 a^{2}$ .

$a^{4} - 12 a^{2} + 4 a^{2} + 16$

Step 8.3.2

Add $- 12 a^{2}$ and $4 a^{2}$ .

$a^{4} - 8 a^{2} + 16$