Pre-Algebra Examples

${(u + 6)}^{2} {(u - 6)}^{2}$

Step 1

Rewrite ${(u + 6)}^{2}$ as $(u + 6) (u + 6)$ .

$(u + 6) (u + 6) {(u - 6)}^{2}$

Step 2

Expand $(u + 6) (u + 6)$ using the FOIL Method.

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Step 2.1

Apply the distributive property.

$(u (u + 6) + 6 (u + 6)) {(u - 6)}^{2}$

Step 2.2

Apply the distributive property.

$(u \cdot u + u \cdot 6 + 6 (u + 6)) {(u - 6)}^{2}$

Step 2.3

Apply the distributive property.

$(u \cdot u + u \cdot 6 + 6 u + 6 \cdot 6) {(u - 6)}^{2}$

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 $u$ by $u$ .

$(u^{2} + u \cdot 6 + 6 u + 6 \cdot 6) {(u - 6)}^{2}$

Step 3.1.2

Move $6$ to the left of $u$ .

$(u^{2} + 6 \cdot u + 6 u + 6 \cdot 6) {(u - 6)}^{2}$

Step 3.1.3

Multiply $6$ by $6$ .

$(u^{2} + 6 u + 6 u + 36) {(u - 6)}^{2}$

Step 3.2

Add $6 u$ and $6 u$ .

$(u^{2} + 12 u + 36) {(u - 6)}^{2}$

Step 4

Rewrite ${(u - 6)}^{2}$ as $(u - 6) (u - 6)$ .

$(u^{2} + 12 u + 36) ((u - 6) (u - 6))$

Step 5

Expand $(u - 6) (u - 6)$ using the FOIL Method.

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Step 5.1

Apply the distributive property.

$(u^{2} + 12 u + 36) (u (u - 6) - 6 (u - 6))$

Step 5.2

Apply the distributive property.

$(u^{2} + 12 u + 36) (u \cdot u + u \cdot - 6 - 6 (u - 6))$

Step 5.3

Apply the distributive property.

$(u^{2} + 12 u + 36) (u \cdot u + u \cdot - 6 - 6 u - 6 \cdot - 6)$

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 $u$ by $u$ .

$(u^{2} + 12 u + 36) (u^{2} + u \cdot - 6 - 6 u - 6 \cdot - 6)$

Step 6.1.2

Move $- 6$ to the left of $u$ .

$(u^{2} + 12 u + 36) (u^{2} - 6 \cdot u - 6 u - 6 \cdot - 6)$

Step 6.1.3

Multiply $- 6$ by $- 6$ .

$(u^{2} + 12 u + 36) (u^{2} - 6 u - 6 u + 36)$

Step 6.2

Subtract $6 u$ from $- 6 u$ .

$(u^{2} + 12 u + 36) (u^{2} - 12 u + 36)$

Step 7

Expand $(u^{2} + 12 u + 36) (u^{2} - 12 u + 36)$ by multiplying each term in the first expression by each term in the second expression.

$u^{2} u^{2} + u^{2} (- 12 u) + u^{2} \cdot 36 + 12 u \cdot u^{2} + 12 u (- 12 u) + 12 u \cdot 36 + 36 u^{2} + 36 (- 12 u) + 36 \cdot 36$

Step 8

Simplify terms.

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Step 8.1

Combine the opposite terms in $u^{2} u^{2} + u^{2} (- 12 u) + u^{2} \cdot 36 + 12 u \cdot u^{2} + 12 u (- 12 u) + 12 u \cdot 36 + 36 u^{2} + 36 (- 12 u) + 36 \cdot 36$ .

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Step 8.1.1

Reorder the factors in the terms $u^{2} (- 12 u)$ and $12 u \cdot u^{2}$ .

$u^{2} u^{2} - 12 u^{2} u + u^{2} \cdot 36 + 12 u^{2} u + 12 u (- 12 u) + 12 u \cdot 36 + 36 u^{2} + 36 (- 12 u) + 36 \cdot 36$

Step 8.1.2

Add $- 12 u^{2} u$ and $12 u^{2} u$ .

$u^{2} u^{2} + u^{2} \cdot 36 + 0 + 12 u (- 12 u) + 12 u \cdot 36 + 36 u^{2} + 36 (- 12 u) + 36 \cdot 36$

Step 8.1.3

Add $u^{2} u^{2} + u^{2} \cdot 36$ and $0$ .

$u^{2} u^{2} + u^{2} \cdot 36 + 12 u (- 12 u) + 12 u \cdot 36 + 36 u^{2} + 36 (- 12 u) + 36 \cdot 36$

Step 8.1.4

Reorder the factors in the terms $12 u \cdot 36$ and $36 (- 12 u)$ .

$u^{2} u^{2} + u^{2} \cdot 36 + 12 u (- 12 u) + 12 \cdot 36 u + 36 u^{2} - 12 \cdot 36 u + 36 \cdot 36$

Step 8.1.5

Subtract $12 \cdot 36 u$ from $12 \cdot 36 u$ .

$u^{2} u^{2} + u^{2} \cdot 36 + 12 u (- 12 u) + 36 u^{2} + 0 + 36 \cdot 36$

Step 8.1.6

Add $u^{2} u^{2} + u^{2} \cdot 36 + 12 u (- 12 u) + 36 u^{2}$ and $0$ .

$u^{2} u^{2} + u^{2} \cdot 36 + 12 u (- 12 u) + 36 u^{2} + 36 \cdot 36$

Step 8.2

Simplify each term.

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Step 8.2.1

Multiply $u^{2}$ by $u^{2}$ 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.

$u^{2 + 2} + u^{2} \cdot 36 + 12 u (- 12 u) + 36 u^{2} + 36 \cdot 36$

Step 8.2.1.2

Add $2$ and $2$ .

$u^{4} + u^{2} \cdot 36 + 12 u (- 12 u) + 36 u^{2} + 36 \cdot 36$

Step 8.2.2

Move $36$ to the left of $u^{2}$ .

$u^{4} + 36 \cdot u^{2} + 12 u (- 12 u) + 36 u^{2} + 36 \cdot 36$

Step 8.2.3

Rewrite using the commutative property of multiplication.

$u^{4} + 36 u^{2} + 12 \cdot - 12 u \cdot u + 36 u^{2} + 36 \cdot 36$

Step 8.2.4

Multiply $u$ by $u$ by adding the exponents.

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Step 8.2.4.1

Move $u$ .

$u^{4} + 36 u^{2} + 12 \cdot - 12 (u \cdot u) + 36 u^{2} + 36 \cdot 36$

Step 8.2.4.2

Multiply $u$ by $u$ .

$u^{4} + 36 u^{2} + 12 \cdot - 12 u^{2} + 36 u^{2} + 36 \cdot 36$

Step 8.2.5

Multiply $12$ by $- 12$ .

$u^{4} + 36 u^{2} - 144 u^{2} + 36 u^{2} + 36 \cdot 36$

Step 8.2.6

Multiply $36$ by $36$ .

$u^{4} + 36 u^{2} - 144 u^{2} + 36 u^{2} + 1296$

Step 8.3

Simplify by adding terms.

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Step 8.3.1

Subtract $144 u^{2}$ from $36 u^{2}$ .

$u^{4} - 108 u^{2} + 36 u^{2} + 1296$

Step 8.3.2

Add $- 108 u^{2}$ and $36 u^{2}$ .

$u^{4} - 72 u^{2} + 1296$